# Equations of Motion (Galileo and Newton)

Galileo did pioneering investigations on the laws of motion and derived the proportionalities shown below.

With the beneft of calculus, Newton, who was born in 1642, the year that Galileo died, developed these proportionalities into the familar equations of motion.

## Newton

### Equation

Distance travelled s at time t assuming continuous, uniform motion (constant velocity v )

s ∝ vt

1

s = vt

Distance travelled s at time t after uniform acceleration a from rest

s ∝ vt

½

s = ½ vt

Velocity v at time t after uniform acceleration a from rest

v ∝ t

a

v = at

Velocity v at time t after uniform acceleration a from initial velocity u

v = u + at

Distance travelled s at time t after uniform acceleration from rest

s ∝ t2

½ a

s = ½ a t2

Distance travelled s at time t after uniform acceleration a from initial velocity u

s = ut + ½ a t2

Print This Page || Home || FAQ || Site Map || Legal || Privacy Promise || Contacts

Woodbank Communications Ltd, South Crescent Road, Chester, CH4 7AU, (United Kingdom)