Question

A 53 kg sprinter, starting from rest, runs a 60 m long race in 7.5 s with a constant acceleration.

How much work does the sprinter do during the first 2.0 s of the race?

What is the sprinter's average power output during the first 2.0 s of the race?

How much work does the sprinter do during the final 2.0 s of the race?

What is the sprinter's average power output during the final 2.0 s  of the race?

Answer 1

here,

mass of sprinter , m = 53 kg

length of track , l = 60 m

time taken , t1 = 7.5 s

a)

let the accelration be a

using seccond equation of motion

l = 0 + 0.5 * a * t1^2

60 = 0 + 0.5 * a * 7.5^2

a = 2.13 m/s^2

for t2 = 2 s

the final speed , v2 = 0 + a * t

v2 = 0 + 2.13 * 2 = 4.26 m/s

using work energy theorm

the work done by the sprinter in 2 s , W2 = 0.5 * m * v2^2

W2 = 0.5 * 53 * 4.26^2 J

W2 = 480.9 J

b)

the sprinter's average power output during the first 2.0 s , P2 = W2 /t2

P2 = 480.9/2 = 240.5 W

c)

at t3 = 7.5 - 2 = 5.5 s

the speed , v3 = 0 + a * t3 = 11.715 m/s

at t4 = 7.5 s

the speed , v4 = 0 + a * t3 = 15.975 m/s

the work done during the final 2 s , W3 = change in kinetic energy

W3 = 0.5 * m * ( v4^2 - v3^2)

W3 = 0.5 * 53 * ( 15.975^2 - 11.715^2)

W3 = 3125.9 J

d)

the average power output , P3 = W3/(t4 - t3)

P3 = 3125.9/2 = 1.56 * 10^3 W