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.

Answer 1

The equations are
v(t)=a*t
and
x(t)=.5*a*t^2

from the statement
15=.5*a*t^2
and
11.5=a*t
plug in a*t from the second equation into the first and solve for t

15=.5*11.5*t (this is actually average speed times the time of the run)
t=30/11.5

knowing t, solve for a
11.5=a*30/11.5
a=11.5^2/30

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