A sprinter accelerates from rest to her top velocity at a rate of 3.80m/s2. After reaching her top velocity, she runs the remainder of the race at constant velocity. She completes the 50.00m long race in 7.88s . How far does the sprinter run while she is accelerating ?

Consider that there are two phases to this problem - an initial acceleration phase and then a constant velocity phase. You can set up the followoing equations:

The distance traveled is:

\frac 1 2 a t_1^2 + v t_2 = 50 m


where a = 3.8m/s^2

The total time is

t_1 + t_2 = 7.88s


The velocity for phase 2 is:

v = a t_1 = 3.88 \frac m {s ^2} t_1


So now you have three equations in three unknowns (v, t_1 and t_2), so you can solve for those values. Then you can answer the question using either of these equations:


v^2 = 2 a d \\
d = \frac 1 2 a t_1^2