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)