Question

1. Towards the end of a 400m race, Faisal and Edward are leading and are both running at 6m/s. While Faisal is 72m from the finish line Edward is 100m from the finish line. Realising this and to beat Faisal, Edward decides to accelerate uniformly at 0.2 m/s2 until the end of the race while Faisal keeps on the same constant speed. Does Edward succeed in beating Faisal?

Answer 1

Answer:

  no

Explanation:

Faisal will finish the race in ...

  (72 m)/(6 m/s) = 12 s

In order to beat Faisal, Edward's average speed in those 12 seconds must exceed ...

  (100 m)/(12 s) = 8 1/3 m/s

To achieve that average speed, Edward's acceleration must be ...

  (8 1/3 m/s -6 m/s)/(12 s/2) = 7/18 m/s² ≈ 0.3889 m/s²

Accelerating at only 0.2 m/s², Edward will not beat Faisal.

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Additional comment

When acceleration is uniform, the average speed is reached halfway through the period of acceleration.