Velocity-Time Graphs

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

Looking at the graph, you can see that velocity in metres per second (m/s) is on the y-axis and time in seconds (s) is on the x-axis.

Velocity-time graphs also show if an object is moving with constant acceleration/deceleration and the magnitude.

Gradient

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

  • 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 represent a constant acceleration – A constant gradient
  • Horizontal lines represent a constant velocity – No acceleration, so the gradient is 0
  • A steepening curve represents an increasing acceleration – An increasing gradient
  • A downwards pointing line represents 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.

The equation to calculate the area of a rectangle is:

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

= 1800 m

The equation to calculate the area of a triangle is:

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

So, the total distance travelled is: 1800 + 600 + 900 = 3300