A speed–time graph with a steep slope shows that the speed is changing rapidly – the acceleration is greater. It follows that we can find the acceleration of an object by calculating the gradient of its speed–time graph:
Acceleration = Gradient of speed – Time graph
The object must be travelling in a straight line; its velocity is changing but its direction is not.
If the speed–time graph is curved (rather than a straight line), the acceleration is changing.
If the graph is sloping downwards, the object is decelerating. The gradient of the graph is negative. So a deceleration is a negative acceleration.
The speed is constant at first (6.0 m/s). Then it increases in equal steps (8.0, 10.0, and so on). In fact, we can see that the speed increases by 2.0 m/s every 10 s. This is enough to tell us that the train’s acceleration is 0.2 m/s2. However, we will follow through the detailed calculation to illustrate how to work out acceleration from a graph.
A = V−U/ΔT
14.0 m/s − 6.0 m/s divided by 60 s−20 s
8.0 m/s divided by 40 s
0.20 m/s raised to 2
The speed–time graph for a skydiver from the moment she leaves an aircraft. She jumps from 5000 m and opens her parachute when she reaches 1500 m, 60 s after she jumps.
There are places where the gradient of the graph is changing (when the graph is not a straight line). To find the acceleration at any moment in time, a tangent to the graph is drawn. This works for any graph: straight or curved.
A graph with Delta :
