Question

A typical male sprinter can maintain his maximum acceleration for 2.0 s, and his maximum speed is 10 m> s. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Assume that his acceleration is constant during the first 2.0 s of the race, that he starts from rest, and that he runs in a straight line.

(a) How far has the sprinter run when he reaches his maximum speed?
(b) What is the magni- tude of his average velocity for a race of these lengths:
(i) 50.0 m;
(ii) 100.0 m;
(iii) 200.0 m?

Answer 1

a) 10m

b)

i)
`v=8.33m/s`

ii)
`v=9.09m/s`

iii)
`v=9.52m/s`

Step-by-step explanation:

The first 2.0s the sprinter maintains a constant acceleration. So we have to use the Constant acceleration motion formulas to solve the first part of the movement, then we need to use the contant velocity motion formulas for the rest of the movement.

a)

`x=Vo*t+(1)/(2)*a*t^2\\\\`

`x=Vo*t+(1)/(2)*(vf-vo)*t\\x=10m`

b)

the sprinter run 10 meters with constant accelaration then it start a constant velocity movement, so:

i) x=50-10=40m

`t=(40m)/(10m/s)=4s`

`v=(50m)/(2s+4s)=8.33m/s`

ii) x=100-10=90m

`t=(90m)/(10m/s)=9s`

`v=(100m)/(2s+9s)=9.09m/s`

iii) x=200-10=190m

`t=(190m)/(10m/s)=19s`

`v=(200m)/(2s+19s)=9.52m/s`