Velocity-Time Graph - Calculating Acceleration

Topic 5 - Forces
Written By Atheridge Tuition
Triple & Combined Science Tag

Figure 1 shows a velocity–time graph for an electric scooter accelerating along a straight road.

Velocity–time graph for an electric scooter showing velocity increasing from 0 to 3 m/s in 2.5 seconds, reaching 4 m/s at 4 seconds, then decreasing to zero at 5 seconds.

Determine the acceleration of the scooter between 0 and 2.5 s.

[2 marks]

  • From the question:

    • Time is between 0 and 2.5 s

    • We care about Velocity, Time and Acceleration (slope of graph)

Velocity–time graph highlighting the section from 0 to 2.5 seconds in pink, showing the scooter accelerating from 0 to 3 m/s.

  • acceleration = change in velocity / time

Acceleration equation triangle showing change in velocity divided by time.

  • Gradient of this graph (known as Rise/ Run using a triangle in Maths):

    • happens to be: change in Velocity / change in Time

    • which is equal to Acceleration (according to the formula above)

    So to find acceleration, we find the gradient

Velocity–time graph showing that acceleration equals the gradient, calculated as rise divided by run. Coloured dashed lines highlight the velocity change and time interval.

  • change in velocity = 3.0 - 0

    = 3.0 m/s

Velocity–time graph highlighting the initial velocity of 0 m/s and final velocity of 3 m/s, showing the change in velocity calculation: 3 − 0 = 3 m/s.
Change in velocity calculation: 3 − 0 = 3 m/s.

    • a = V / t

    • 3.0 / 2.5 = 1.2 m/s²

Worked acceleration calculation using the velocity–time graph: change in velocity of 3 m/s divided by 2.5 seconds gives an acceleration of 1.2 m/s².
 

Continue Revising Paper 2

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