During the start of a 100 m sprint, Carmelita Jeter (a top US sprinter) pushes o

Question

During the start of a 100 m sprint, Carmelita Jeter (a top US sprinter) pushes off against the starting blocks for a total duration of 0.5 s. She applies a force that increases linearly from 0 N to 2200 N over the first 0.25 s, and then averages 2200 N over the remaining 0.25 s (see the graph below). If her mass is 67 kg, and she was initially at rest, what was her velocity at the instant that she left the starting blocks? (Area of a rectangle = base*height; Area of a triangle = 12*base*height) (3 pts)

Explanation / Answer

use:
change in momentum = area of F-t curve

Area of F-t curve = area of reactangle + area of triangle
= 2200*0.25 + 0.5*(0.25)*2200
= 825 Ns

so,
change in momentum = 825 Ns
m*(vf-vi) = 825
67*(vf-0) =825
vf = 825/67
= 12.3 m/s
Answer: 12.3 m/s

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