# Exam-Style Question on Speed Time Graph

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 670. This question is similar to one that appeared on a GCSE Higher paper in 2020. The use of a calculator is allowed.

Here is a speed-time graph for a drone.

(a) Work out an estimate for the distance the train travelled between the 10th and 15th second.

Is your answer to part (a) an underestimate or an overestimate of the actual distance the train travelled during that time? Give a reason for your answer.

Noah used the graph to find out an estimate for the deceleration of the drone at time 35 seconds. He realised that it took ten seconds for the drone's speed to fall to zero.
Here is Noah’s working.

$$\text{deceleration = speed ÷ time}$$ $$= 16 \div 10$$ $$= 1.6 m/s²$$

(b) Noah’s method does not give a good estimate of the deceleration at time 35 seconds. Explain why.

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