An 84.0 kg sprinter starts a race with an acceleration of 1.76 m/s2. if the sprinter accelerates at that rate for 11 m, and then maintains that velocity for the remainder of the 100 m dash, what will be his time (in s) for the race?

t=17.838s

Explanation:

The displacement is divided in two sections, the first is a section with constant acceleration, and the second one with constant velocity. Let's consider the first:

The acceleration is, by definition:

So, the velocity can be obtained by integrating this expression:

The velocity is, by definition: , so

.

Do x=11 in order to find the time spent.

At this time the velocity is:

This velocity remains constant in the section 2, so for that section the movement equation is:

The left distance is 89 meters, and the velocity is , so:

So, the total time is 14.303+3.5355s=17.838s