Completing calculations on curves
You will need to be able to explain and complete calculations on curves in both distance-time and velocity-time graphs. This example uses a velocity-time graph.
Look at the graph and explain the motion of the vehicle between 60 and 120 seconds.
- Look at the vertical \(\text{y}\)-axis. You need to check what type of graph it is before you start answering.
- Between 60 and 85 seconds the graph is curving upwards. This means that the velocity is increasing at an increasing rate. In other words the vehicle is accelerating non-uniformly.
- The graph is rising in a reasonably straight line between 85 and 95 seconds. This represents uniform or constant acceleration.
- In between 95 and 120 seconds the graph is curving to become a horizontal line. This means that the acceleration is becoming less, ie the velocity is increasing at a reducing rate.
If you’re sitting the higher tier exam, you might be asked to work out the average acceleration or the distance travelled over the curved region. To calculate the average acceleration, draw a straight line (shown in green) and find the gradient.
Remember, gradient = acceleration.
Acceleration = (15 – 0) ÷ (120 – 60) = 0.25 m/s2.
To find the distance travelled, find the area under the triangle made by the green line.
Distance travelled (area under line) = ½ × (120 – 60) × 15 = 450 m