Velocity-Time Graphs

Velocity-time graphs show us how an object’s velocity changes over time. You can see an example of a velocity-time graph below.

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A graph plotting velocity (in metres per second) against time (in seconds). The graph showcases three distinct phases: 'Constant acceleration' from 0 to 20 seconds, where velocity increases linearly; 'Constant velocity' from 20 to 60 seconds, where the velocity remains steady at around 60 m/s; and 'Constant deceleration' from 60 to 90 seconds, where velocity decreases linearly.

  • In the graph, velocity (measured in m/s) is on the y-axis and time (in seconds) is on the x-axis.

Velocity-time graphs also show if an object has constant acceleration or deceleration, as well as its magnitude.

Gradient

We can calculate the acceleration of an object by using the equation:

An equation defining acceleration. It reads: 'Acceleration equals the change in velocity divided by the time taken', with 'Change in velocity' as the numerator and 'Time taken' as the denominator.

A mathematical equation representing acceleration. It reads: 'a equals Δv over t', where 'a' stands for acceleration, 'Δv' represents change in velocity, and 't' denotes time.

  • a = Acceleration in metres per second squared (m/s2)
  • Δv = Change in velocity in metres per second (m/s)
  • t = time taken in seconds (s)

Features of Velocity-Time Graphs

When looking at velocity-time graphs, we can observe important features:

  • Straight lines indicate a constant acceleration – A constant gradient
  • Horizontal lines indicate a constant velocity – No acceleration, so the gradient is 0
  • A steepening curve indicates an increasing acceleration – An increasing gradient
  • A downward-sloping line indicates deceleration – The object is slowing down, so there is a negative gradient

Distance Travelled

To calculate the distance travelled, we can calculate the area under the curve. With the example below, we can separate the area into two triangles and a rectangle.

A graph plotting velocity in metres per second against time in seconds. The graph shows a red triangle from 0 to 30 seconds, indicating a rise in velocity, a constant yellow rectangle between 30 to 60 seconds, indicating steady velocity, and a red triangle from 60 to 90 seconds, indicating a decrease in velocity.

The equation to calculate the area of a rectangle is:

A formula stating that the area of a rectangle is equal to its width multiplied by its length.

The area of the rectangle = (50 − 20) × (60 − 0) = 30 × 60

= 1800 m

The equation to calculate the area of a triangle is:

A formula stating that the area of a triangle is equal to half the product of its base and height.

Area of triangle 1 = 0.5 × (20 − 0) × (60 − 0) = 0.5 × 20 × 60

= 600 m

Area of triangle 2 = 0.5 × (80 − 50) × (60 − 0) = 0.5 × 30 × 60

= 900 m

Therefore, the total distance travelled is 3,300 m (1,800 m + 600 m + 900 m).

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