How far has the sprinter run when he reaches his maximum speed? Please show the

Question

How far has the sprinter run when he reaches his maximum speed?

Please show the work so I can understand how it works, thanks!

A typical male sprinter can maintain his maximum acceleration for 2.1s and his maximum speed is 10m/s . After reaching this maximum speed, his acceleration becomes zero and then he runs at constant speed. Assume that his acceleration is constant during the first 2.1s of the race, that he starts from rest, and that he runs in a straight line. How far has the sprinter run when he reaches his maximum speed? What is the magnitude of his average velocity for a race of the following lengths: (i) 50.0 m , (ii) 100.0 m , (iii) 200.0 m ?

Explanation / Answer

Part A)

Apply f = vo + at

10 = 0 + a(2.1)

a = 4.76 m/s^2

d = vot + .5at^2

d = (0) + (.5)(4.76)(2.1)^2

d = 10.5 m

Part B)

to run 50 m, we have 39.5 m left at 10 m/s

d = vt

39.5 = 10t

t = 3.95 sec

Total time = 2.1+3.95 = 6.05 sec

v = 50/6.05

v = 8.26 m/s

to tun 100 m

89.5 = 10t

t = 8.95 + 2.1 = 11.05 sec

v = 100/11.05 = 9.05 m/s

to run 200 m

189.5 = 10t

t = 18.95 + 2.01 = 20.96 sec

v = 200/20.96

v = 9.54 m/s

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