# SUVAT equations ```SUVAT equations
Objective – To be able to use and
derive the SUVAT equations for
motion with constant acceleration
Starter
Calculate;
1) The acceleration in the first two seconds
2) The distance travelled in the last 4 seconds
3) The total displacement in the first 16 seconds
The SUVAT equations (also known as the equations of constant
acceleration) are 5 equations which link the following quantities:
s = displacement (m)
u = initial velocity (ms-1)
v = final velocity (ms-1)
a = acceleration (ms-2)
t = time (s)
Velocity
Derive an equation for v in terms of u, a
and t based on this graph:
v
u
O
t
Time
Velocity
Derive an equation for v in terms of u, a and t
based on this graph:
graph
a= change in y
change in x
a= (v-u)
t
at=v-u
v
u
O
t
Time
v=u+at (1)
Velocity
Equation 2 – from area under the
graph
Hint: Distance = speed x time
v
Area = &frac12; base x height
= &frac12; t x (v-u)
u
Area = base x height
= ut
O
t
Time
Velocity
Equation 2 – from area under the
graph
Area of triangle = &frac12;t (v-u)
substitute in v-u=at
= &frac12; at2
Area of rectangle = ut
so total area under graph
v
Area = &frac12; base x height
= &frac12; t x (v-u)
u
= ut + &frac12;at2
Area = base x height
= ut
O
t
Time
s= ut + &frac12;at2 (2)
Velocity
Equation 3, from average velocity
v
u
O
t
Time
Velocity
Equation 3, from average velocity
average velocity = u+v
2
v
av velocity = displacement
time
therefore,
u+v = s
2 t
u
O
t
Time
s = u+v x t (3)
2
Equation 4, from equations 1 and3
v=u+at,
s=u+v x t
2
Equation 4, from equations 1 and3
v=u+at,
s=u+v x t
2
Multiply: a = (v-u) with
s=u+v x t
t
2
as = &frac12; (u+v) x t x (v-u)
t
Cancel out t and multiply out terms:
2as = (v+u)(v-u) = v 2 + uv –uv - u 2
v 2 = u 2 + 2as (4)
Equation 2, from equations 1 and3
v=u+at,
s=u+v x t
2
Equation 2, from equations 1 and3
v=u+at,
Sub
v=u+at, into s=u+v x t
2
s=(u+u+at) x t
2
s= 2ut + at2
2
2
s=ut + &frac12;at2 (2)
s=u+v x t
2
Equation 5, from equations 1 and3
v=u+at,
Sub
u=v -at, into s=u+v x t
2
s=(v+v-at) x t
2
s= 2vt - at2
2
2
s=vt - &frac12;at2 (5)
s=u+v x t
2
SUVAT equations:
v=u+at (1)
s= ut + &frac12;at2 (2)
s = u+v x t (3)
2
v 2 = u 2 + 2as (4)
s= vt - &frac12;at2 (5)
Using SUVAT equations
• In a standard problem, you are given three of
the 5 quantities
• You then have to work out a fourth (with the
5th quantity unknown)
• Choose an equation which misses out the
unknown
Example 1:
A rocket lifts off from rest with an acceleration of
20ms-2. How fast will it be travelling after 50s?
Example 2:
A car is travelling at 8ms-1 . It accelerates at 1ms-2 for a
distance of 18m. How fast is it then travelling?
Worked examples:
A rocket lifts off from rest with an acceleration of 20ms-2. How
fast will it be travelling after 50s?
Step 1: write down what you know
a = 20ms-2, u = 0ms-1, t = 50s, v = ?
Step 2: choose a suitable equation
v=u+at
Step 3: Substitute the numbers into the equation
v = 0 + (50 x 20) = 1000ms-1
Worked examples:
Example 2:
A car is travelling at 8ms-1 . It accelerates at 1ms-2 for a distance
of 18m. How fast is it then travelling?
Worked examples:
```