A speed-time graph represents the motion of an object by showing how its speed changes over time. On this graph, the vertical axis represents speed, while the horizontal axis represents the time taken. The gradient of the graph represents the rate of change of speed with respect to time (acceleration or deceleration), and the area under the graph represents the total distance travelled by the object.
See how acceleration, uniform speed, deceleration and distance travelled are represented on one graph.
A speed-time graph shows how an object's speed changes as time progresses. The vertical axis represents speed, \(v\), and the horizontal axis represents time, \(t\).
The gradient of a speed-time graph represents the rate of change of speed with respect to time, which is acceleration.
\[\text{Acceleration} = \dfrac{\text{Change of speed}}{\text{Change in time}}\]
Choose appropriate scales for both axes, plot the coordinate points \((t, v)\), then join the points using a ruler or a smooth curve.
Construct a speed-time table by calculating speed values for given time intervals, then plot the points and join them.
The area under the graph equals the distance travelled. Common shapes are rectangles, triangles and trapeziums.
\[\text{Area under speed-time graph} = \text{Distance travelled}\]
\[\text{Average speed} = \dfrac{\text{Total distance}}{\text{Total time}}\]
Read the question, answer it in your mind, then press “Check Answer”.
A car accelerates uniformly from rest to a speed of \(20\text{ m s}^{-1}\) in \(5\text{ seconds}\). What is its acceleration?
What does the area under a speed-time graph represent?
A motorcycle travels at a uniform speed of \(15\text{ m s}^{-1}\) for \(8\text{ seconds}\). Calculate the distance travelled during this period.
Calculating distance from the area under a scaled speed-time graph, step by step.
For a speed-time graph, the area under the graph = the distance travelled over the same time interval. Split the area into triangles, rectangles and trapeziums, work out each area, then add them.
Make sure the time unit in the speed matches the unit on the time axis before calculating.
The graph below shows the motion of a car over 15 seconds. Calculate (a) the rate of change of speed for the first 5 seconds, (b) describe the motion for the second 5 seconds, and (c) the total distance travelled.
The area under the graph is divided into trapezium \(A\), rectangle \(B\) and trapezium \(C\).
If an answer has to be rounded, use the exact value in any later calculation, not the rounded one. For example, if the exact total distance is \(\dfrac{454}{15} = 30.2\overline{6}\) km and is rounded to \(30.27\) km, then the average speed over 36 minutes is \(\dfrac{454/15}{0.6} = 50.44\) km h\(^{-1}\) — not the \(30.27 \div 0.6 = 50.45\) km h\(^{-1}\) you get from the rounded value.
A negative gradient means the object is moving backwards or in the opposite direction.
The object is still moving forward in the same direction; only its speed is decreasing (decelerating).
A speed of zero means the graph stops.
A speed of zero means the object is momentarily stationary; time continues to increase along the horizontal axis.
Complete all parts first, then press the check answer button.
1 What does the gradient of a speed-time graph represent?
2 A car travels with a speed that decreases from \(25\text{ m s}^{-1}\) to \(0\text{ m s}^{-1}\) in \(5\text{ seconds}\). What is its deceleration?
3 The total distance travelled by an object is determined by calculating the under its speed-time graph.
4 On a speed-time graph, a horizontal straight line with zero gradient indicates that the object is moving at a speed.
Drag each graph feature to the correct physical meaning. On a phone, tap the answer choice first, then tap the meaning box.
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