Area under a velocitytime graph

1
Area under a velocity-time graph
Car travelling at 70 mph for 2 hours
2 70
Area
140
This is the distance travelled, 140 miles
The area under a velocity-time graph gives the
distance travelled (displacement)
2
Gradient of a velocity-time graph
The gradient of a velocity-time graph gives the
acceleration.
Car accelerating steadily from 0 to 20 ms-1 in 5
seconds
Acceleration
4 ms-2
This is 4 ms-1 per second
Area of triangle
50 m
Distance travelled 50 metres
3
Summary
The gradient of a velocity-time graph gives the
acceleration
The area under a velocity-time graph gives the
displacement
Area of a triangle
Area of a trapezium
4
Object with velocity increasing steadily from u
to v in time t
Acceleration a
Equation 1
Displacement s
Equation 2
5
Equation 1
Equation 2
Substituting for v
Equation 3
6
Equation 1
Rearranging for t
Equation 2
Substituting for t
Equation 4
7
Constant Acceleration Equations