Question

The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity the sprinter had after 2 seconds. 

a. Determine the sprinter's constant acceleration during the first 2 seconds. 

b. Determine the sprinters velocity after 2 seconds have elapsed. 

c. Determine the total time needed to run the full 100 meters.

d. On the axes provided below, draw the displacement vs time curve for the sprinter.

Answer 1

a. For the first 2 seconds, while acceleration is constant, d = ½at² Substituting the given values d = 10 meters, t = 2 seconds gives a = 5 m/s²

b. The velocity after accelerating from rest for 2 seconds is given by v = at, so v = 10 m/s 

c. The displacement, time, and constant velocity for the last 90 meters are related by d = vt. To cover this distance takes t = d/v = 9s. The total time is therefore 9 + 2 = 11 seconds