This document summarizes key kinematic equations for a particle moving in a straight line with constant acceleration: 1) The acceleration is equal to the change in velocity divided by the change in time. 2) Displacement is equal to the average speed multiplied by time. 3) Final velocity squared is equal to initial velocity squared plus two times acceleration times displacement.

1. Chapter 2 – Kinematics of a particle
moving in a straight line
s = displacement (m)
u = initial velocity (ms-1)
v = final velocity (ms-1)
a = acceleration (ms-2)
t = time (s)
When acceleration is constant
change in velocity v-u
acceleration=
change in time t
Rearranging gives
v=u+at i

2. displacement = average speed x time
u+v
s= t (ii)
2
Rearranging (i) to make t the subject and substituting
into (ii) gives
u+v v-u v 2 -u 2
s= =
2 a 2a
Rearranging gives
v 2 =u 2 +2as (iii)

3. We have
u+v
s= t (ii) and v=u+at i
2
Substituting (i) into (ii) gives
u+u+at 2u at 1
s= t= + t= u+ at t
2 2 t 2
1 2
s=ut+ at (iv)
2
Similarly u=v-at
v-at+v 2v at 1
s= t= t= v- at t
2 2 t 2
1 2
s=vt- at (v)
2