Rectilinear Motion

Important Terms And Definitions

1. Kinematics : It is the branch of dynamics which deals

with the forces acting on bodies in motion without considering the mass of a body and the forces which is responsible to cause the motion.

Rectilinear Motion

Motion of a particle along a straight line is called rectilinear motion, linear motion or one dimensional motion.

3.

To describe linear motion of a particle its position at all times is to be specified. The equations used in this case are called ‘Equations of Motion’ or ‘Kinematical equations’.

4. Every motion is related to the observer:

Position of a particle in motion is described in terms of distance from reference point or origin.

Path length or distance travelled : The total distance covered by a particle

during its motion is called path length or distance traveled (scalar quantity)

Displacement : Change in position of a moving particle

in a particular direction is called displacement. Displacement is the shortest distance between two positions of a moving particle in a particular direction (vector quantity)

Displacement and distance traveled are equal in rectilinear motion but distance traveled is greater than displacement in any other motion.

Average velocity (vector quantity)

The average velocity of a moving particle is defined as the displacement divided by the interval in which it has occurred

x

avg vel Vt

Average speed : Average speed of a moving particle is defined as total distance travelled divided by time taken

Avg speed V = total distance traveled / time

Acceleration : Acceleration of a moving body is defined as the rate of change of velocity with respect to time.

Equation of motion, when Distance (s) Travelled by a Body Moving with a Uniform Velocity:

We know that, Distance travelled = Average velocity x time

we have, v = u + at, substitute this in equation (1), we get

u v

S t2

Equation of Motion, when Velocity of a Body Moving with Uniform Acceleration after Covering a Distance ‘S’

Equation of Motion, when a Distance Travelled in nth Second by a

particle (or Body) Moving with Uniform Acceleration:

Consider a body in rectilinear motion moving with initial velocity (u) and uniform acceleration (a). In nth

second, it acquires a velocity (v) and covers a distance (s).

u = Initial velocity of a body: v = Final velocity of a body n = Number of second: sn = Distance travelled in n sec.

sn-1 = Distance covered in (n – 1) sec.

snth = Distance travelled in nth sec.

= sn – sn-1

A = Uniform acceleration. From Equation (2), we have

For distance travelled in n second, put t = n

For distance travelled in (n – 1) second, put t = n – 1

Graphical Representation

Velocity Time Graph Case I Uniform velocity Area under the curve = displacement S = Vt

Case II:- When the body moves with a variable velocity:

If velocity varies from 0 to v, V-T diagram is a triangle as shown in fig. Here initial velocity (u) is zero.

Area under the graph = Area of a triangle

= s = distance travelled.

= s = distance travelled.

s = distance travelled.

If velocity varies from u to 0. (Final velocity (v) is zero): V-T

diagram is a triangle as shown in Area under the graph = Area of a rectangle

2

1OB OA

2

1u t

2

1v at t ....sinceu = v - at

2

10 at t ....since v = 0

2

1at

2

s distance travelled

Negative sign indicates that there is retardation.

uSlope tan

t

ua .....since -a = retardation.

t

If velocity varies from u to v: V-T diagram is trapezium as shown in fig. Area under the graph = Area of trapezium