Area under a velocity-time graph

1. v mph 70 0 2 t hours 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. vms-1 20 0 t seconds 5 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. b a h h b 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. v Velocity u t 0 Time 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. Equation 1 where u = initial velocity v= final velocity Equation 2 a = acceleration Equation 3 t = time taken s = displacement Equation 4 Constant Acceleration Equations