One simple model for a person running the 100 m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of

Complete Question:

One simple model for a person running the 100 m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of 11.5 m/s in 2.24 s, what will be his total time?

Answer:

total time = 6.24 s

Explanation:

Using the equation of motion:

v = u + at

initial speed, u = 0 m/s

v = 11.5 m/s

t = 2.24 s

11.5 = 0 + 2.24a

a = 11.5/2.24

a = 5.13 m/s²

For the total time spent by the sprinter:

s = ut + 0.5at²

100 = 0.5 * 5.13 * t²

t² = 100/2.567

t² = 38.957

t = √38.957

t = 6.24 s