# Equations of motion

We consider two types of accelerated motion:
(a) uniform acceleration where the velocity changes steadily with time, and
(b) non-uniform acceleration where the rate of change of velocity is changing with time (see acceleration file).

## Equations of motion for uniform acceleration

If the acceleration of a particle is uniform the following equations apply to its motion:

average velocity = [v+u]/2
acceleration (a) = [v-u]/t
s = ut + ½ at2
v2 =u2+2as

where u is the initial velocity, v the final velocity, a the acceleration, t the time taken and s the displacement.

In any problem concerning these equations you would be given three quantities and asked to work out the fourth

Example problems
1. A dragster starts from rests and accelerates at 25 ms-2 for 4 s. Calculate:
(a) the final velocity
(b) the distance travelled
(a) v = u + at = 0 + 25x4 = 100 ms-1
(b) s = ½ at2 = 0.5 x 25 x 16 = 200 m

2. A ball travelling at 20 ms-1 is hit by a bat and returned along its original path but in the opposite direction at 35 ms-1.
If the ball was in contact with the bat for 0.02 s calculate:
(a) the acceleration of the ball during the hit
(b) the distance moved by the ball during the hit
(a) a = [v-u]/t = [35-(-20)]0.02 = 55/0.02 = 2750 ms-2
(b) v2 =u2+2as
s = [352 – 202]/2x2750 = 0.15 m

Remember that the above set of equations can ONLY BE USED FOR UNIFORM ACCELERATED MOTION.

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