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.
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)
