A sprinter can accelerate with constant acceleration for 4.00 s before reaching top speed. He can run the 100 m dash in 10 s. What is his speed as he crosses the finish line?

12.5 m/s

Explanation:

If the avg speed is 10 m/s we assume that the speed is constant and not fluctuating

If VT (Velocity*Time) is equal to speed at the end of the 4 seconds of accel. it is the top speed at the finish line

since the speed is 0 at the beginning of races, we will use V0= 0 m/s

So the avg velocity for those 4 seconds is (VT+V0) /2 = or 1/2 VT (for 40% of the race)

The avg velocity for the last 6 seconds is, of course, VT (for 60% of the race

hence

(1/2VT)(.4) + VT(.6) = 10 m/s

VT = 10/.8 = 12.5 m/s