Equations of motionWe 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 accelerationIf the acceleration of a particle is uniform the following equations apply to its motion: average velocity = [v+u]/2acceleration (a) = [v-u]/ts = ut + at2v2 =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 problems1. 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 = 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.Equations of motion proofIn studying the motion of objects it is often helpful to use an equation to work out the velocity, acceleration or the distance travelled.

We use the following letters to represent certain quantities:

Distance travelled