# 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?**

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?**

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.

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

The velocity from 0-5s is 10ms^{-1}. The velocity from 5-9s is:

**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?**