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Difference Between Speed and Velocity

Difference Between Speed and Velocity

Edited By Vishal kumar | Updated on Jul 02, 2025 04:42 PM IST

The rate of change of position of an object with time in any direction is called its speed. speed has only magnitude and no direction, so it is a scalar quantity. Different types of speeds exist. The speedometer of an automobile indicates its instantaneous speed at any instant.

The rate of change of position of an object with time in a given direction is called its velocity. Velocity has both magnitude and direction, so it is a vector quantity. Different types of velocity exist.

In this article, we will discuss speed, and types of speed, velocity and types of velocity, speed and velocity difference with numerical examples. Speed and velocity is an important topic in Class 9 physics, It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams.

This Story also Contains
  1. What is Speed?
  2. Velocity
  3. Solved Examples Based on Speed And Velocity
Difference Between Speed and Velocity
Difference Between Speed and Velocity

What is Speed?

Speed is the quantity which shows how fast the body is moving. It does not have any direction associated with it.

Formula to calculate speed:

 Speed = Distance/Time 

Numerical example:

1- If a body covers a distance of 18m in 1 sec then, find the speed of the body.

The speed of a body is calculated using the formula:

 Speed = Distance  Time 


Here, the distance covered is 18 meters, and the time taken is 1 second. Plugging in the values:

 Speed =18 m1 s=18 m/s


So, the speed of the body is 18 m/s.

After speed, now let's shift to the concept of average and instantaneous speed.

Average Speed and Instantaneous Speed

Average Speed: Amount of total distance covered in total time.

Mathematically average speed can written as,

Average Speed = Total Distance Traveled  Total Time Taken 

Numerical example:

A body covers a total distance of 50 m with variable speed in 5 sec. Find the average speed.

 Average Speed = Total Distance  Total Time 

Substituting these values:

 Average Speed =50 m5 s=10 m/s

Tips to Calculate Average Speed

The formula for average speed when a body covers two distances s1 and s2 in times t1 and t2 respectively is:

Vavg=s1+s2t1+t2

Instantaneous Speed:

It is the speed at that particular instant or small interval of time.

Mathematically,

 Instantaneous Speed =limΔt0ΔsΔt

where:

  • Δs is the displacement over a very small time interval Δt,
  • limΔt0 represents taking the limit as the time interval approaches zero.

Also read -

Velocity

Velocity is the rate of change of displacement. It is the displacement in unit time. It is a vector quantity. The S.I. unit of measurement of velocity is ms-1.

 Velocity = Displacement  Time 

where:

  • Displacement is the change in position of the object in a specific direction,
  • Time is the time taken for the displacement to occur.
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Now let's understand about the concept of average and instantaneous velocity.

Average Velocity and Instantaneous Velocity

Average Velocity: Amount of total displacement covered in total time.

 Average Velocity = Total Displacement  Total Time 


If the displacement is represented by Δs and the total time by Δt, then:

 Average Velocity =ΔsΔt

Instantaneous Velocity: It is Velocity at that particular instant or small interval of time.

Instantaneous Velocity =dsdt
where:

  • dsdt is the derivative of displacement s with respect to time t,
  • This derivative represents how displacement changes over an infinitesimally small time interval, giving the velocity at that exact moment.

Relation between Speed and Velocity:

Speed and velocity have many similaities and differences between them. But majorly direction is the main point of difference between them. Basically, speed do not contain direction but velocity conatins direction. Here we will discuss the similarities and difference between speed and velocity in detail. "Velocity is speed with displacement," asserts the relationship between speed and velocity.

Similarities between speed and velocity:

  • Both speed and velocity are ways of calculating an object's change in position over time.
  • In practice, an object's speed and velocity are the same in a straight line motion. Since distance and displacement will be the same.
  • Because they are both physical quantities, they can both be measured and quantified.
  • The units of speed and velocity are the same, metres per second or m/s.

Difference between speed and velocity:

Definition :

  • Speed : It is the rate at which an object covers distance.
  • Velocity : The rate at which an object changes its position (displacement) in a specific direction.

Type of Quantity :

  • Speed : It is a Scalar quantity (only has magnitude, no direction)
  • Velocity : It is a Vector quantity (has both magnitude and direction).

Formula :

  • Speed: Speed = Distance  Time 
  • Velocity: Velocity = Displacement  Time 

Direction :

  • Speed : Does not indicate any direction.
  • Velocity : It indicates the direction of motion.

Values :

  • Speed : Always positive or zero. Can never be negative.
  • Velocity : This can be positive, negative, or zero, depending on direction.

Example :

  • Speed : "A car travels at 60 km/h."
  • Velocity : "A car moves north at 60 km/h."

Above points will help the students to distinguish between the speed and the velocity.

Recommended Topic Video

Solved Examples Based on Speed And Velocity

Example 1: A body travels 100 km southwest and then 502 km in the northern direction. The total magnitude of the velocity if the time taken is 1hr.

1) 100+502 km/hr
2) 100−502 km/hr
3) 502 km/hr
4) 100 km/hr

Solution:

As we learned,

Average Velocity = Total Displacement Total time taken

So,

Thus, the average velocity is calculated as:

 Average Velocity = Total Displacement  Total Time =502 km1hr=502 km/hr

Example 2: An object moving with a speed of 6.25 ms−1, is decelerated at a rate given by dvdt=−2.5v where v is the instantaneous speed. The time taken (in seconds) by the object, to come to rest, would be:

1) 2

2) 1

3) 4

4) 8

Solution:

Step 1: Separate Variables
Rewrite the equation by separating v and t :

dvv=2.5dt


Step 2: Integrate Both Sides
Integrate both sides to find v as a function of t :

1vdv=2.5dt


This yields:

lnv=2.5t+C


Step 3: Solve for the Constant C
At t=0, the initial speed v=6.25 m/s :

ln(6.25)=C
So, C=ln(6.25).

Step 4: Substitute C and Solve for t when v=0
Now, the equation becomes:

lnv=2.5t+ln(6.25)


To solve for t when v0, take the limit of both sides as v approaches zero:

2.5t=ln(6.25)


Solving for t :

t=ln(6.25)2.52 seconds 

Hence, the answer is option (1).

Example 3: A particle moves such that its position vector r^(t)=cos⁡ωti^+sin⁡ωtj^ where ω is a constant and t is time. Then which of the following statements is true for the velocity v→(t) and acceleration a→(t) of the particle :
1) v→ and a→ both are parallel to r→
2) v→ is perpendicular to r→ and a→ is directed away from the origin
3) v→ and a→ both are perpendicular to r→
4) v→ is perpendicular to r→ and a→ is directed towards the origin

Solution:

Given r(t)=cos(ωt)i^+sin(ωt)j^
1. Velocity v(t) : Calculating v(t), we get v(t)=ωsin(ωt)i^+ωcos(ωt)j^, which is perpendicular to r(t) (dot product =0 ).
2. Acceleration a(t) : Calculating a(t), we get a(t)=ω2r(t), meaning a(t) is directed towards the origin.

Hence, the answer is the option (4).

Example 4: A particle moves 50 m in 5 seconds, then 20 m in the next 4 seconds and 30 m in the next 7 seconds, then the average speed (in m/s ) of the particle is :

1) 6.25

2) 7.25

3) 8.50

4) 5

Solution:

Step 1: Calculate Total Distance and Total Time
- Total Distance =50+20+30=100 m
- Total Time =5+4+7=16 s

Step 2: Calculate Average Speed

 Average Speed = Total Distance  Total Time =10016=6.25 m/s

Hence, the answer is the option (1).

Example 5: A particle travelled first 10 m with 2 m/s, the next 10 m with 3 m/s and the last 10 m with 6m/s then its average speed is (in m/s) :

1) 3

2) 4

3) 5

4) 6

Solution:

Total Distance =10+10+10=30 m


Total Time =102+103+106=10 seconds


Average Speed = Total Distance  Total Time =3010=3 m/s

Hence, the answer is the option (1).

Frequently Asked Questions (FAQs)

1. Define Speed.

Speed is the rate of change of distance or the distance travelled in unit time. It is a scalar quantity. The Unit of measurement of speed is ms-1.


speed(v)=distance travelled(d)/Time taken(t)   


Where, v is the speed, d is the distance travelled and t is the time taken.

2. Define Velocity.

Velocity is the rate of change of displacement. It is the displacement in unit time. It is a vector quantity. The unit of measurement of velocity is ms-1.


velocity=displacement/Time taken 

3. What are the distinguish between speed and velocity?

Difference between speed and velocity or Speed vs velocity:

SpeedVelocity
  • The term "speed" refers to the rate at which a thing moves.

  • The velocity of an object describes how fast it is travelling as well as in which direction it is moving.

  • The rate at which an object moves along a path is called speed

  • The rate and direction of an object's movement are known as velocity.

  • Example: A car's speed has been stated if it is said to operate at 80 km/h.

  • Example: The car's velocity has been stated if it is said to be approaching at 80 km/h to the north.


  • A scalar quantity is speed.

  • A vector quantity is velocity.

The above table gives difference between speed and velocity

4. What are the similarities between speed and velocity?

Speed and velocity similarities:

  • Both speed and velocity are ways of calculating an object's change in position over time.

  • In practice, an object's speed and velocity are the same in a straight line motion. Since distance and displacement will be the same.

  • Because they are both physical quantities, they can both be measured and quantified.

  • The units of speed and velocity are the same, metres per second or m/s.

5. What are the difference between Motion and Speed?

Difference between Motion and Speed:

  • A change in the location of an object over time is referred to as motion. Displacement, distance, velocity, acceleration, time, and speed are all terms used to describe motion. 

  • The ratio of distance to time (a scalar quantity) is the average speed. Speed is unconcerned about direction.

6. Why is velocity considered a vector quantity while speed is a scalar quantity?
Velocity is considered a vector quantity because it includes both magnitude (speed) and direction. It requires both these components to be fully described. Speed, on the other hand, is a scalar quantity because it only describes the magnitude of motion, without regard to direction.
7. How can an object have zero velocity but non-zero speed?
An object cannot have zero velocity and non-zero speed simultaneously. If an object has any speed, it must be moving in some direction, which means it has a non-zero velocity. Zero velocity implies the object is at rest, which means it has zero speed as well.
8. Can velocity be negative? If so, what does it mean?
Yes, velocity can be negative. A negative velocity doesn't mean the object is moving slower or backwards in a literal sense. It simply indicates that the object is moving in the opposite direction to what is defined as the positive direction in the given coordinate system.
9. What is the main difference between speed and velocity?
Speed is a scalar quantity that measures how fast an object is moving, regardless of direction. Velocity is a vector quantity that measures both how fast an object is moving and in what direction. In other words, speed tells you only the rate of motion, while velocity includes both the rate and the direction of motion.
10. Can an object have a constant speed but changing velocity?
Yes, an object can have a constant speed but changing velocity. This occurs when an object moves at a constant rate but changes direction. For example, a car driving around a circular track at a constant speed has a changing velocity because its direction is constantly changing, even though its speed remains the same.
11. What is the relationship between average speed and average velocity?
Average speed is the total distance traveled divided by the total time taken, regardless of direction changes. Average velocity is the displacement (change in position) divided by the time taken. They are equal only when the motion is in a straight line without any direction changes or when the starting and ending points are the same.
12. Can an object's speed change even if its velocity remains constant?
No, if an object's velocity remains constant, its speed must also remain constant. Constant velocity means both the speed (magnitude) and direction remain unchanged. Any change in speed would result in a change in the magnitude of the velocity vector.
13. How can an object have a high speed but low velocity?
An object can have a high speed but low velocity if it moves quickly but doesn't cover much distance in a straight line. This can happen when an object moves in a circular path or zigzags. The speed (distance/time) might be high, but the velocity (displacement/time) could be low if the net displacement is small.
14. What's the difference between instantaneous speed/velocity and average speed/velocity?
Instantaneous speed/velocity refers to the speed/velocity at a specific moment in time, while average speed/velocity is calculated over a period of time. Instantaneous values give you information about the motion at a precise point, whereas average values provide an overall picture of the motion over a given interval.
15. How can you have a non-zero average speed but zero average velocity?
You can have a non-zero average speed but zero average velocity if you end up at the same point where you started, despite having moved during the time interval. For example, if you run around a circular track and return to the starting point, your average speed is positive (distance/time), but your average velocity is zero (displacement/time, where displacement is zero).
16. How does acceleration relate to changes in speed and velocity?
Acceleration is the rate of change of velocity over time. It can result from changes in speed, direction, or both. An object accelerates when its speed increases or decreases, or when it changes direction, even if its speed remains constant. Changes in speed alone affect both speed and velocity, while changes in direction affect only velocity.
17. How does the concept of relative motion affect measurements of speed and velocity?
Relative motion affects measurements of speed and velocity because these quantities depend on the frame of reference. The same motion can have different speed and velocity values when measured from different reference frames. For instance, a person walking on a moving train has one velocity relative to the train and another relative to the ground.
18. How does the idea of frame of reference impact our understanding of speed and velocity?
The frame of reference is crucial in understanding speed and velocity because these quantities are relative. The same motion can be described differently depending on the chosen reference frame. For example, a person walking on a moving train has one velocity relative to the train and another relative to the ground. This concept highlights that there's no absolute motion; all motion is relative to some frame of reference.
19. How does the concept of relative velocity apply to everyday situations?
Relative velocity is commonly experienced in everyday situations. For example, when you're in a moving car and pass another car, the relative velocity between the cars is the difference between their velocities. If you're walking on a moving walkway in an airport, your velocity relative to the ground is the sum of your walking velocity and the walkway's velocity. Understanding relative velocity helps in navigation, sports (like in ball games where players are moving), and even in understanding how we perceive motion in our daily lives.
20. Can you explain how speed and velocity are related to the concept of work in physics?
In physics, work is defined as the product of force and displacement in the direction of the force. This definition involves velocity rather than speed because it considers the direction of motion. The work done on an object can change its velocity (both magnitude and direction), which in turn affects its kinetic energy. While speed is directly related to kinetic energy, velocity is more relevant when calculating work, especially when the force and displacement are not in the same direction.
21. How do speed and velocity relate to the concept of impulse in physics?
Impulse is defined as the change in momentum of an object. Since momentum is the product of mass and velocity, impulse is more directly related to velocity than to speed. The impulse-momentum theorem states that the impulse applied to an object equals its change in momentum. This involves changes in velocity (both magnitude and direction) rather than just speed. Understanding the vector nature of velocity is crucial when analyzing impulse in collisions or other force interactions, especially when the forces are not aligned with the initial velocity.
22. Why is it important to specify a reference point when discussing velocity?
Specifying a reference point is crucial when discussing velocity because velocity is a relative measure. The same motion can be described differently depending on the chosen reference point. For example, a passenger walking in a moving train has different velocities relative to the train and relative to the ground.
23. How does the concept of velocity apply to objects moving in two or three dimensions?
In two or three dimensions, velocity is represented as a vector with components in each dimension. For example, in 2D, velocity would have x and y components, while in 3D, it would have x, y, and z components. The magnitude of this vector is the speed, and its direction is the direction of motion.
24. What role does displacement play in understanding the difference between speed and velocity?
Displacement is key to understanding the difference between speed and velocity. Speed considers the total distance traveled, regardless of the path taken. Velocity, however, only considers the displacement (the straight-line distance between the start and end points). This is why velocity gives information about direction, while speed does not.
25. Why is it incorrect to say "velocity per hour" or "speed per second"?
It's incorrect to say "velocity per hour" or "speed per second" because velocity and speed already include time in their definitions. Velocity is displacement per unit time, and speed is distance per unit time. Saying "per hour" or "per second" would be redundant and mathematically incorrect. The correct terms would be "meters per second" or "kilometers per hour," for example.
26. How does the direction of motion affect calculations of speed and velocity?
Direction of motion doesn't affect calculations of speed, as speed is just the magnitude of how fast an object is moving, regardless of direction. However, direction is crucial for velocity calculations. When calculating average velocity, you must consider the displacement (which accounts for direction) rather than the total distance traveled.
27. Can an object's velocity change even if its speed remains constant?
Yes, an object's velocity can change even if its speed remains constant. This happens when the object changes direction while maintaining the same speed. For example, a car moving around a curve at a constant speed has a changing velocity because its direction is continuously changing.
28. How do speed and velocity relate to the concept of distance and displacement?
Speed relates to distance, while velocity relates to displacement. Speed is calculated using the total distance traveled, regardless of the path taken. Velocity, on the other hand, is calculated using displacement, which is the straight-line distance between the start and end points. This is why velocity includes direction information, while speed does not.
29. Why is it possible to have a higher average speed than average velocity for a given journey?
It's possible to have a higher average speed than average velocity for a given journey because average speed considers the total distance traveled, while average velocity only considers the displacement (straight-line distance between start and end points). If the path taken is not a straight line, the total distance will be greater than the displacement, resulting in a higher average speed compared to average velocity.
30. How does the concept of vectors help in understanding velocity?
The concept of vectors is crucial in understanding velocity because velocity is a vector quantity. Vectors have both magnitude and direction, just like velocity. This allows us to represent velocity as an arrow, where the length of the arrow represents the speed (magnitude) and the direction of the arrow represents the direction of motion. Vector addition also helps in understanding how velocities combine in more complex motions.
31. What's the significance of the slope of a position-time graph in relation to speed and velocity?
The slope of a position-time graph represents the velocity of the object. If the graph is a straight line, the slope (and thus the velocity) is constant. The steeper the slope, the greater the velocity. A positive slope indicates motion in the positive direction, while a negative slope indicates motion in the negative direction. The magnitude of the slope at any point gives the instantaneous speed.
32. How do speed and velocity differ when describing circular motion?
In circular motion, speed typically remains constant (if it's uniform circular motion), while velocity is constantly changing. This is because speed only considers how fast the object is moving, which doesn't change in uniform circular motion. However, velocity includes direction, which is continuously changing as the object moves around the circle. This results in a constant acceleration towards the center of the circle, even though the speed doesn't change.
33. Can you explain the concept of velocity in terms of rate of change of position?
Velocity can be understood as the rate of change of position with respect to time. Mathematically, it's the derivative of position with respect to time. This means velocity tells us how quickly and in what direction an object's position is changing at any given moment. The magnitude of this rate of change is the speed, while the direction of the change gives the direction of motion.
34. Why is it important to consider both speed and velocity in physics problems?
Considering both speed and velocity is important because they provide different information about an object's motion. Speed tells us how fast an object is moving, which is useful for calculations involving time and distance. Velocity gives us both speed and direction, which is essential for understanding the object's motion in space and for calculations involving forces and acceleration. Using the appropriate quantity ensures accurate analysis and problem-solving in physics.
35. How does the concept of instantaneous velocity differ from average velocity?
Instantaneous velocity is the velocity of an object at a specific instant in time, while average velocity is calculated over a period of time. Instantaneous velocity is determined by finding the limit of the average velocity as the time interval approaches zero. It gives the velocity at a precise moment, which is useful for understanding motion at specific points. Average velocity, on the other hand, provides an overall picture of the motion between two points in time.
36. Can you explain how speed and velocity are related to the concept of momentum?
Speed and velocity are closely related to momentum, but in different ways. Momentum is defined as the product of an object's mass and its velocity. This means that momentum is a vector quantity, like velocity, having both magnitude and direction. The magnitude of momentum is related to speed (mass times speed), but the full description of momentum requires the directional information provided by velocity. This is why changes in either speed or direction can affect an object's momentum.
37. How do speed and velocity factor into calculations of kinetic energy?
In calculations of kinetic energy, speed is the key factor, not velocity. Kinetic energy is given by the formula KE = (1/2)mv^2, where m is mass and v is speed. Although v is often used to represent velocity in other formulas, in this case, it represents speed. This is because kinetic energy is a scalar quantity and doesn't depend on the direction of motion. Whether an object is moving north or south, its kinetic energy will be the same as long as its speed and mass are the same.
38. Why is it that velocity can be zero even when speed is not, but speed can never be zero if velocity is not?
Velocity can be zero when speed is not zero in situations where an object returns to its starting point. In this case, the displacement is zero, making the average velocity zero, even though the object has moved and thus has a non-zero average speed. However, speed can never be zero if velocity is not zero because velocity includes speed as its magnitude. If an object has any velocity, it must be moving in some direction, which means it has a non-zero speed.
39. Can you explain how speed and velocity are represented in vector notation?
In vector notation, velocity is represented as a vector quantity, typically denoted by v⃗ (v with an arrow above it). It can be broken down into components, such as v⃗ = vxi⃗ + vyj⃗ + vzk⃗ in three dimensions, where vx, vy, and vz are the velocity components in the x, y, and z directions respectively, and i⃗, j⃗, and k⃗ are unit vectors in these directions. Speed, being a scalar, is represented by the magnitude of the velocity vector, denoted as |v⃗| or simply v (without the arrow).
40. How do speed and velocity relate to the concept of acceleration?
Acceleration is the rate of change of velocity over time. This means it can result from changes in speed, direction, or both. An increase or decrease in speed results in acceleration, as does a change in direction even if the speed remains constant. While speed is involved in acceleration (as part of velocity), the full concept of acceleration requires understanding velocity, as it accounts for changes in both the magnitude and direction of motion.
41. Why is it important to distinguish between speed and velocity in projectile motion problems?
In projectile motion problems, distinguishing between speed and velocity is crucial because the object's speed and velocity behave differently throughout its trajectory. While the speed of a projectile may change due to gravity, its velocity is constantly changing in both magnitude and direction. Understanding this helps in analyzing the motion at different points, calculating the range and height of the projectile, and determining factors like the time of flight. The vertical and horizontal components of velocity are often treated separately in these problems, which requires a clear understanding of velocity as a vector quantity.
42. How does the relationship between speed and velocity change in non-uniform motion?
In non-uniform motion, the relationship between speed and velocity becomes more complex. While speed always represents the magnitude of how fast an object is moving, velocity can change even if speed remains constant (due to changes in direction), or velocity can remain constant while speed changes (if the change in speed is exactly balanced by a change in direction). In non-uniform motion, instantaneous speed and velocity become more relevant than average values, and the rate of change of these quantities (acceleration) becomes a key factor in describing the motion.
43. How do speed and velocity factor into the concept of centripetal acceleration?
In circular motion, an object experiences centripetal acceleration, which is directed towards the center of the circle. The magnitude of this acceleration is given by a = v^2/r, where v is the speed of the object and r is the radius of the circle. Although this formula uses speed, the concept is intimately related to velocity because centripetal acceleration is causing a continuous change in the direction of the velocity vector, even when the speed remains constant. This illustrates how an object can have constant speed but changing velocity in circular motion.
44. Why is it that changing velocity always results in acceleration, but changing speed doesn't necessarily mean acceleration?
Changing velocity always results in acceleration because acceleration is defined as the rate of change of velocity over time. Since velocity is a vector quantity, a change in either its magnitude (speed) or direction results in acceleration. However, changing speed doesn't necessarily mean acceleration in all reference frames. For example, an object moving in a circle at constant speed is accelerating (due to the changing direction of its velocity) from the perspective of an observer outside the circle, but from the object's own rotating reference frame, it might be considered as moving at constant velocity.
45. Can you explain how the concepts of speed and velocity are used in defining and understanding waves?
In wave motion, both speed and velocity are important concepts. The speed of a wave refers to how fast the disturbance travels through the medium, while the velocity includes the direction of propagation. For mechanical waves, the speed is determined by the properties of the medium. In more complex scenarios, like electromagnetic waves, the concept of phase velocity (the rate at which the phase of the wave propagates in space) and group velocity (the velocity of

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