Physics Question?

Question

A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter and how long does it take her to reach that speed? Please show/explain work clearly.

Answer 1

Assuming uniform acceleration:
v(avg) = [v(zero) + v(final)]/2
v(avg) = (0 + 11.5)/2 = 5.75m/s

Use D = rt to find the time:
t = D/r = 15/5.75 = 2.6087sec

Use the displacement formula to find the acceleration:
s = (1/2)at^2
a = 2s/t^2
a = 2(15)/(2.6087)^2
a = 4.408m/s^2