Equations of Motion

Equations of Motion

In the previous section, the formula above was used to calculate the Acceleration of a moving object. In the Higher course, this formula is more commonly written in the following way :-


v = u + at


This formula is one of three equations of motion. The following two formulae complete the set :-


s = ut + 1/2at2

v2 = u2 + 2as

Where :-

u = Initial Speed (ms-1)

v = Final Speed (ms-1)

a = Acceleration (ms-2)

s = Displacement (m)

t = Time (s)

Note - The derivation of the three Equations of Motion are non-examinable but can be found in the Graphs of Motion section.

Through using a combination of the above formulae, lots of information about a moving object can be found.

Example 1 -

A ball is dropped from rest. If it hits the ground 2 seconds later, what is its Velocity on impact?

u = 0 ms-1

v = ?

a = - 9.8 ms-2

s = ?

t = 2 s

v = u + at

v = 0 + ( - 9.8 x 2 )

v = - 19.6 ms-1

v = 19.6 ms-1 ( downwards )


Example 2 -

A Stone is dropped into a well and takes 3.5 seconds to strike the water. What is the depth of the well?

u = 0 ms-1

v = ?

a = - 9.8 ms-2

s = ?

t = 3.5 s

s =

s = ( 0 x 3.5 ) + ( 0.5 x -9.8 x 3.52 )

s = - 60 m

s = 60 m deep


Example 3 -

A ball is thrown vertically upwards at 12 ms-1. How high is the highest point in its motion ?

u = 12 ms-1

v = 0 ms-1

a = - 9.8 ms-2

s = ?

t = ?

v2 = u2 + 2as

s = (v2 - u2) / 2a

s = (0 - 144) / (2 x -9.8)

s = 7.35 m

s = 7.35 m (upwards)