# Equation of motion

There are three important equations of motion, that is:

v = u + at

s = ut + 1/2at2

V2 = u2 + 2as

Here ‘u’ is the initial velocity, ‘v’ is the final velocity, ‘a’ is the uniform acceleration and ‘s’ is the displacement of the object. These equations apply to a object moving with a uniform acceleration.

 Example A car moving at a speed of 10 ms-1 comes to rest in 2 seconds. Find its retardation. Solution In velocity of the car, u = 10 m s-1 Final velocity of the car, v = 0 m s-1 Time taken by the car to come to rest, t = 2s ∴ Acceleration of the car, a = v-u/t = 0 – 10/2 = -5m s-2 Hence, retardation of the car = 5 m s-2.
 Example A bus accelerates uniformly at 8 m s-2 from rest. Find its velocity at the end of 10 seconds. Solution Given acceleration of the bus, a = 8 s-2. Initial velocity of the bus, u = 0 m s-1 Time interval, t = 10 s. ∴Final velocity of the car, v = u + at                                                  = 0 + ( 8 ) ( 10 )                                                  = 80 m s-1.

## Graphical Representation of Motion

Motion of a object can be represented by graphs . These give the visual representation of motion of the object. There are three types of graphs, that is s – t, v – t and a – t graphs. Here , we discuss s – t and v – t graphs

### Displacement – Time Graph

In this graph, displacement is plotted along y-axis and time along x-axis .

Example :

 Time in (s) 0 1 2 3 4 5 Displacement in (m) 0 5 10 15 20 25

Significance of Displacement – Time Graph

1. Displacement of a particle at any instant of time can be determined.
2. Nature of motion of the particle can be studied.
3. Slope of the graph at any point gives the instantaneous velocity of the object.

### Velocity – Time Graph

If velocity is plotted along y – axis and time along x – axis, then the graph is called  v-t graph .

Example:

 Time in (min) 0 1 2 3 4 5 6 7 8 Velocity in ( m s-1) 5 10 15 20 20 20 15 10 5