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Have you ever watched a car moving on a highway or a ball falling straight to the ground? These everyday examples involve motion in a straight line a fundamental concept in physics. In this chapter, you will explore how objects move in a single direction and learn to describe their motion using mathematical tools.These NCERT Notes are prepared by subject experts following the latest CBSE syllabus.
Motion in a Straight Line, also known as rectilinear motion, forms the basis of kinematics the branch of mechanics that deals with the motion of objects without knowing the causes of motion. This chapter is important for your school exams, JEE, and NEET preparation. The NCERT notes for class 11 the Physics explain important topics such as position, displacement, Instantaneous Velocity and Speed, acceleration and Relative Velocity . You will also learn how to draw motion graphs, and understand the equations of motion for uniformly accelerated motion.
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The NCERT Class 11 Physics Chapter 2 Notes Motion in a Straight Line provide brief explanations and focusing on the understanding of the main concepts such as displacement, velocity, acceleration, and Equation of Motion. These notes are ideal to study quickly and also vital in studying for examinations like CBSE, JEE and NEET.
An object is said to be at rest if it remains stationary in relation to a specific frame of reference over time. On the other hand, if an object's position relative to a frame of reference changes over time, it is said to be in motion. A coordinate system to which observers attach coordinates to describe events and observations is referred to as a frame of reference.
The magnitude of displacement may or may not be equal to the length of the path.
When an object returns to its original position along a path with a non-zero length, displacement can be zero. Displacement takes into account the change in position regardless of the total distance travelled, as well as the direction of motion.
(a) Uniform speed: A particle moves at uniform speed when it covers equal distances in equal intervals of time, regardless of how small those intervals are. For example, a car travels an equal distance of 5 metres per second, indicating a uniform speed of 5 m/s. Uniform speed denotes a constant rate of motion with no acceleration or deceleration during the time intervals specified.
(b) Non-uniform (variable) speed: A particle with non-uniform (variable) speed travels unequal distances in equal time intervals. For example, a car travels 5m in the first second, 8m in the second second, 10m in the third second, 4m in the fourth second, and so on. This variation in distance covered indicates that the particle's speed varies for each one-second interval, confirming that it moves at a variable speed. Variable speed denotes that the rate of motion varies over time.
(c) Average speed: The average speed (Vavg) of a particle for a given interval of time is defined as the ratio of the total distance travelled (d) to the total time taken (t).
(d) Instantaneous speed: It is the speed of a particle at a specific point in time. When we talk about "speed," we usually mean instantaneous speed.
(1) Uniform velocity: The condition in which both the magnitude and direction of an object's velocity remain constant is referred to as uniform velocity. This occurs when the particle continues to move in the same straight line without changing direction. To put it another way, a particle with uniform velocity must travel at a constant speed along a straight path with no change in motion.
(2) Non-uniform velocity: Changes in the magnitude or direction of the velocity, or both, characterise non-uniform velocity. The particle's speed and/or direction of motion may change in this scenario. Non-uniform velocity indicates that the object is not moving in a straight line at a constant speed, but rather has variations in its motion over time.
(c) Average velocity: It is defined as the ratio of the body's displacement to the time it takes.
(d) Instantaneous velocity: Instantaneous velocity is defined as the rate of change of the position vector of a particle with respect to time at a specific instant.
In real-life motion, the speed or velocity of an object may not remain constant throughout its journey. To understand how fast an object is moving at a particular instant of time, we define the concepts of instantaneous speed and instantaneous velocity.
Instantaneous speed is the speed of an object at a particular moment of time. It is the limit of average speed as the time interval approaches zero. In simpler terms, it tells us how fast an object is moving at an instant.
where
Instantaneous speed is a scalar quantity and is always positive.
Instantaneous velocity is defined as the velocity of an object at a particular instant of time. Like instantaneous speed, it is obtained by taking the limit of the average velocity as the time interval tends to zero.
where
Instantaneous velocity is a vector quantity and has both magnitude and direction.
(a) Uniform acceleration: Uniform acceleration refers to a situation in which both the magnitude and direction of the acceleration of a body remain constant during its motion.
(b) Non-uniform acceleration: A body is said to have non-uniform acceleration if there are changes in either the magnitude or direction of acceleration, or both, during its motion.
(c) Average acceleration: The average acceleration of an object is defined as the change in velocity per unit time.
Position-Time, Velocity-Time, and Acceleration-Time Graph
Parameters |
p-t Graph |
v-t Graph |
a-t Graph |
X and Y axis |
Time and Position |
Time and Velocity |
Time and Acceleration |
Slope |
It gives the velocity of an object |
It gives the acceleration of an object. |
It gives push of a moving object. |
Straight slope |
It gives uniform velocity |
It gives uniform acceleration | The slope of an a–t graph represents the rate of change of acceleration with time |
Curvy Slope |
Change in velocity |
Change in acceleration |
Change in the amount of push |
p-t graph
v-t graph
Using the velocity-time graph of the object under uniformly accelerated motion, we can derive some simple set of equations that relate displacement
1. Derivation of velocity-time relation
The slope of the graph gives the acceleration a of the object.
2. Derivation of displacement-time relation
The area under this curve is
Area of
Area of
Area of rectangle
and as explained in the previous section, the area under
But
Substituting this value in the above equation, we get
or
Derivation of velocity-displacement relation
Now, the area of trapezium
From equation (i), we get
Substituting this value of
So the three kinematic equations of uniformly accelerated motion that we have derived so far are
The relative velocity of an object
if
then the relative velocity of
Similarly, the relative velocity of
Distance is a scalar quantity representing the total path length traveled by an object, regardless of direction. Displacement, on the other hand, is a vector quantity that denotes the shortest straight-line distance from the initial to the final position, including direction.
Yes, velocity can be negative. The sign of velocity indicates direction. For example, if an object moving to the right is considered positive, then motion to the left would be negative velocity.
An object is accelerating uniformly if its velocity changes by equal amounts in equal intervals of time. This is typically indicated by a straight line with a constant slope on a velocity-time graph
Understanding motion in a straight line is fundamental to physics as it lays the groundwork for more complex motions and dynamics. It helps in analyzing and predicting the behavior of objects under various forces and is essential for solving real-world problems in mechanics.
In uniform motion, an object covers equal distances in equal intervals of time, resulting in a constant velocity. In non-uniform motion, the object covers unequal distances in equal intervals, indicating a change in velocity over time
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