## The Equations of Motion

If a body acceleratesuniformly, analysis of the motion of the body becomes muchsimplified. We can use any of five equations of motion:

(1)

(2)

(3)

(4)

(5)

where s=distance travelled,u=initial speed, v=final speed, a=acceleration and t=time.

Assuming (1) and (5), theothers are easily proved.

To prove (2) substitute (5)into (1)

To prove (3) rearrange (1)to give u=v-at and substitute into (5)

To prove (4) rearrange (1)to giveandrearrange (5) to give Multiplythe equations together:

so

The equations of motion areused by writing down which ofyouhave and which you want to find. On this basis you can decide whichequation you need to use.

Suppose a car starts fromrest and accelerates to a speed of 10m/s in 20m. Find theacceleration

We look which of theequations hasItis