MOTION IN A STRAIGHT LINE, CBSE CLASS XI, PHYSICS NOTES PART-II

 CBSE CLASS 11, MOTION IN A STRAIGHT LINE, PHYSICS NOTES-(PART II)

MOTION IN A STRAIGHT LINE


According to the CBSE Syllabus 2025-26

CBSE Class 10 Science Chapter 10th Motion in a Straight Line Notes

Study Material and Notes of Ch 2 Motion in a Straight Line World Class 10th Science

ACCORDING TO THE CBSE SYLLABUS 2025-26, THIS CHAPTER HAS BEEN RENUMBERED AS CHAPTER 2

UNIFORM SPEED AND UNIFORM VELOCITY

UNIFORM SPEED.

An object is said to move with uniform speed if it covers equal distances in equal intervals of time, however small these intervals of time may be.

UNIFORM VELOCITY.

An object is said to move with uniform velocity if it covers equal displacements in equal intervals of time, however small these intervals of time may be.

VARIABLE SPEED AND VARIABLE VELOCITY

Variable Speed.

An object is said to move with variable speed if it covers unequal distances in equal intervals of time, however small these intervals of time may be.

Variable Velocity.

An object is said to move with variable velocity if it covers unequal displacements in equal intervals of time, however small these intervals of time may be.

AVERAGE SPEED AND AVERAGE VELOCITY

Average Speed.

It is the ratio of total path length traversed and the corresponding time interval.
Or

“Total distance covered in unit time is called average speed.”

Average speed = Total distance covered / total time taken

Average speed = Total distance / total time taken

 
Average velocity

Average velocity is the displacement divided by the time interval in which the displacement occurs.

0R

“It is that signle velocity with which the object can travel the same length in the same time as it generally does with varying velocity”.

Average velocity = Total displacement / total time taken

The average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval.

INSTANTANEOUS SPEED AND INSTANTANEOUS VELOCITY

Instantaneous Speed.

The speed of an object at an instant of time is called instantaneous speed.
Or
“Instantaneous speed is the limit of the average speed as the time interval becomes infinitesimally small”.

Instantaneous velocity

The instantaneous velocity of a particle is the velocity at any instant of time or at any point of its path.
or
“Instantaneous velocity or simply velocity is defined as the limit of the average velocity as the time interval Δt becomes infinitesimally small.”

ACCELERATION

The rate at which velocity changes is called acceleration.

UNIFORM ACCELERATION

If an object undergoes equal changes in velocity in equal time intervals it is called uniform acceleration.
AVERAGE AND INSTANTANEOUS ACCELERATION

Average Acceleration.

It is the change in the velocity divided by the time-interval during which the change occurs.

Instantaneous Acceleration.

It is defined as the limit of the average acceleration as the time-interval Δt goes to zero.

  

KINEMATICAL GRAPHS

The ‘displacement-time’ and the ‘velocity-time’ graphs of a particle are often used to provide us with a visual representation of the motion of a particle. The ‘shape’ of the graphs depends on the initial ‘co-ordinates’ and the ‘nature’ of the acceleration of the particle (Fig.)




            

  Curves (a) and (c) represent motion with a constant speed u. Curves (b) and (d) represent motion with a uniform acceleration a starting with an initial speed u.

The following general results are always valid
(i) The slope of the displacement-time graph at any instant gives the speed of the particle at that instant.
(ii) The slope of the velocity-time graph at any instant gives the magnitude of the acceleration of the particle at that instant.
(iii) The area enclosed by the velocity-time graph, the time-axis and the two co-ordinates at ,time instants t1 to t2 gives the distance moved by the particle in the time-interval from t1 to t2.
Equations of Motion for Uniformly Accelerated Motion
For uniformly accelerated motion, some simple equations can be derived that relate displacement (x), time taken (f), initial velocity (u), final velocity (v) and acceleration (a). Following equation gives a relation between final and initial velocities v and u of an object moving with uniform acceleration a: v = u + at

Suppose a body is projected vertically upward from a point A with velocity u. If we take upward direction as positive

(i) At time t, its velocity                               v = u – gt

(ii) At time t, its displacement from A is given by

(iii) Its velocity when it has a displacement ‘h’ is given by

                                              v2 = u2 – 2gh

(iv) When it reaches the maximum height from A, its velocity v = 0. This happen when t = u / g . The body is instantaneously at rest at the highest points.

(v) The maximum height reached


(vi)  Total time to go up and return to the point of projection = 2u / g

(vii) At any point C between A and B, where AC = S, the velocity v is given by

 

In some problems, it is convenient to take the downward direction as positive; in such a case, all the measurements in the downward direction are considered as positive, i.e., acceleration will be +g. But sometimes we may need to take upward as positive, and in such a case, acceleration will be -g.

RELATIVE VELOCITY

Relative velocity of an object A with respect to another object B is the time rate at which the object A changes its position with respect to the object B.

VAB = VA - VB

The relative velocity of two objects moving in the same direction is the difference in the speeds of the objects.
The relative velocity of two objects moving in opposite directions is the sum of the speeds of the objects.

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