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Area under a velocity-time graph Car travelling at 70 mph for 2 hours Area = This is the distance travelled, 140 miles 2 70 = 140 v mph t hours 0 2 70 The area under a velocity-time graph gives the distance travelled (displacement)

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Car accelerating steadily from 0 to 20 ms -1 in 5 seconds Distance travelled = 50 metres = 50 m Acceleration = = 4 ms -2 v ms -1 t seconds 0 5 20 Area of triangle Gradient of a velocity-time graph This is 4 ms -1 per second The gradient of a velocity-time graph gives the acceleration.

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Summary The area under a velocity-time graph gives the displacement The gradient of a velocity-time graph gives the acceleration Area of a triangle Area of a trapezium b h b h a

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Object with velocity increasing steadily from u to v in time t Acceleration a Velocity Time 0 t u v Equation 1 Displacement s Equation 2

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Equation 1 Equation 2 Substituting for v : Equation 3

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Equation 1 Equation 2 Rearranging for t : Equation 4 Substituting for t :

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Equation 1 Equation 2 Equation 3 Equation 4 Constant Acceleration Equations where u = initial velocity v = final velocity a = acceleration t = time taken s = displacement

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