Equations of Motion

Consider an object moving with uniform acceleration, a. Let u be the initial velocity (at time t = 0), v, velocity after time t and S, displacement during this time interval. There are certain relationships between these quantities.

Acceleration = Change in velocity / Time interval

a = (v - u)/t

v = u + at

This is called as the first equation of motion.

Displacement = (average velocity) × (time interval)

s = (v + u)/2 × t

s = (u + at + u)/2 × t

s = ut + ½at2

This is called the second equation of motion.

If object starts from rest, u = 0

s = ½at2

Thus, the displacement of an object undergoing a constant acceleration is proportional to t2, while the displacement of an object with constant velocity (zero acceleration) is proportional to t.


a = (v - u)/t and s = (v + u)/2 × t

Multiply them

a.s = (v2 - u2)/2

v2 = u2 + 2as

This is called as third equation of motion. In case of motion under gravity a can be replaced by g.