A-level Physics (Advancing Physics)/Graphs/Worked Solutions

1. In the following distance-time graph, what is the velocity 4 seconds after the beginning of the object's journey? Distance-time graph example.png

At this point, the graph is a straight line. So:

2. What is the velocity at 12 seconds?

Approximately, there is a rough straight line at this point. The object is travelling towards home 2 ms−1 each second (look at the previous second, for example). So, its velocity is -2 ms−1.

3. In the following velocity-time graph, how far does the object travel between 7 and 9 seconds? Velocity-time graph example.png

Distance travelled is equal to the area under the graph. Between 7 and 9 seconds, this is the shaded area of the graph. So, calculate the area of the triangle:

4. What is the object's acceleration at 8 seconds?

There is a straight line between 7 and 9 seconds which we can use to answer this question. The acceleration is equal to the gradient of the graph, so:

5. A car travels at 10ms−1 for 5 minutes in a straight line, and then returns to its original location over the next 4 minutes, travelling at a constant velocity. Draw a distance-time graph showing the distance the car has travelled from its original location.

10ms−1 = 600 metres / minute.

Distance-time graph question.png

6. Draw the velocity-time graph for the above situation.

The velocity from 0-5s is 10ms−1. The velocity from 5-9s is:

Velocity-time graph question.png

7. The velocity of a ball is related to the time since it was thrown by the equation . How far has the ball travelled after 2 seconds?