How Does a Sprinter's Acceleration Affect Race Time?

[SuperCass]

Homework Statement

A world-class sprinter accelerates to his maximum speed in 3.8 s. He then maintains this speed for the remainder of a 100-m race, finishing with a total time of 10.4 s.

(a) What is the runner's average acceleration during the first 3.8 s?

(b) What is his average acceleration during the last 6.6 s?

(c) What is his average acceleration during the entire race?

(d) State why your answer to part (c) is not the average of the answers to parts (a) and (b).

Homework Equations

Kinematic Equations

The Attempt at a Solution

I know that part b is 0 because the runner maintains a constant velocity. But for parts a, c, and d, I'm not sure what to do. I know I have to find the distances he runs while his speed changes and when it is constant and then find the acceleration, but how do I do this?


Thank you so much for your help!

 

[rl.bhat]

Assume a as acceleration and v as the maximum velocity.
Using the kinematic equations
Find v(max) in terms of a and t1
Find x1 in terms of a and t1.
In the second part the velocity is constant.
So x2 = v(max)*t2.
Then put x1 + x2 = 100 m, and solve for a and v(max).