Question

A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5m/s) in the first a5.0m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach this speed?

Answer 1

In general you need two standard equations:

(1) Vt = Vo + a*t, with Vo the speed at start (here 0);
(2) Xt = Xo + Vo*t + a/2*t^2

As Xo and Vo are 0, both equations reduce to:

(1.1) Vt = a*t
(1.2) Xt = a/2 * t^2

where Vt = 11.5 m/s and Xt = 5.0 m. This gives two equations with two unknowns (acceleration a and time-to-destination t). These are exactly the two variables asked for. Solve this system of equations and find a and t.