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

NO

Explanation:

To determine this, we have to firstly determine the time it took Faisal to complete the race with 72 meters left and then the speed Edward used for the final 100 meters (with both distance occurring at the same point in time).

To determine the time it took Faisal from that onward, we use the formula

Speed = distance/time

Since Faisal maintained his speed at the end of the race, the speed will be 6 m/s while distance at the end to be covered his 72 m. Thus

6 = 72/time

time = 72/6

time = 12 seconds; It will take Faisal 12 seconds to complete the race from that point.

For Edward, he accelerated uniformly (for 0.2 m/s²) after running at a constant speed of 6 m/s. Thus, the time it would have taken him to complete (at a speed of 6 m/s) the final 100 m would be

speed = distance/time

6 = 100/time

time = 100/6

time = 16.67 s.

However, he accelerated uniformly at 0.2m/s², hence to get the speed, the formula; speed = acceleration × time will be used

speed = 0.2 × 16.67

speed = 3.334 m/s

To determine the time it took Edward from 100 meters away,

speed = distance/time

3.334 = 100/time

time = 100/3.334

time = 29.94 seconds

It would have taken Edward 29.94 seconds to complete the race, hence he would not have succeeded in defeating Faisal

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