Equations of Motion

Use of suvat to solve problems

Defining Motion

·      Displacement, s (m) is the vector equivalent of distance – it is distance moved in a certain direction

·      This is average velocityv = velocity (ms-1)
s = displacement (m)
t = time (s)

v=  s/t

Velocity, v (ms-1) is the vector equivalent of speed – it is the speed in a given direction


·      This is instantaneous velocityv = velocity (ms-1)
_s = change in displacement (m)
_t = change in time (s)

v=  _s/_t

Another way of describing this is to think of velocity as the rate of change of displacement:


·      a = acceleration (ms-2)
v = final velocity (ms-1)
u = initial velocity (ms-1)
t = time (s)

a=  _v/_t=(v-u)/t

The rate of change of velocity is called acceleration – this is also a vector:


·      This equation assumes that acceleration is constant or uniform

Equations of Motion (suvat)

·      Problem solving strategy
1.	Write a list of all the quantities in order; 
s =
u =
v =
a =
t =

2.	Write in any values you know, leaving blank what you don’t or have to find
3.	Choose one of the equations that has in it what you know AND what you need
4.	Solve the equation!

s=  1/2 (u+v)t
s=ut+  1/2 at^2
v^2= u^2+2as

These simple equations can be used to derive four equations that allow any problem involving an object moving under constant acceleration to be solved. They are given on your data sheet but it is best if you learn them:



Vertical and Horizontal Components of Velocity

·      Because velocity is a vector, like force, we can take horizontal and vertical components in the same way

·      Horizontal and vertical components of velocity are independent of each other

·      You can use the equations of motion with the horizontal or vertical components of velocity


Objects projected horizontally
Horizontal component of velocity
This is unaffected by g 
The initial velocity, u is the horizontal component
The horizontal component of u is unchanged throughout the flight (neglecting air resistance)
Vertical component of velocity
This is subject to g
The initial velocity, u is always 0ms-1
The time taken to is the same for both the horizontal and vertical components
Objects projected vertically
Horizontal component of velocity
This is 0ms-1
Vertical component of velocity
Acceleration is g (it is usual for it to be -9.81 taking upward to be positive and downward to be negative)
The initial velocity, u is the vertical component of the projection velocity
The velocity = 0ms-1 at the maximum height reached. It is useful to make this the final velocity, v
This is halfway through the time of flight

You are expected to deal with 2 types of problem at AS level:



Displacement-Time Graphs

Velocity-Time Graphs

The area under the graph gives the distance travelledThe gradient of a straight line gives the accelerationAt any point on a curve, draw a tangent and find the gradient to calculate the acceleration at that point