(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 50 kg sprinter, starting from rest, runs 50 m in 7.0 s at constant acceleration.

a. What is the magnitude of the horizontal force acting on the sprinter?

b. What is the sprinter's power output at 2.0 s, 4.0 s and 6.0 s?

2. Relevant equations

xf= xo + vt+ 0.5*a*t^2

F= ma

vf= vi + at

P= (delta Work)/(Delta t)

P= f*d*cos angle

3. The attempt at a solution

Using the distance, initial velocity, and time I solve for acceleration

xf= xo + vt+ 0.5*a*t^2

50 = 0 + 0+ 0.5*a*(7^2)

a= 2.04 m/s^2

Therefore, F=ma=50 (2.04)=102 N

This, I got right. But when I calculate the power, I'm not getting the right answer when i use the first equation.

I calculate the velocity at t= 2s, and I get

vf = vi + at

vf= 2.04 ( 2)

vf= 4.08 m/s

Therefore work=delta kinetic energy= 0.5 m (vf^2 - vi^2)

K= 0.5 ( 50) ( 4.08^2)

K= 416.16 J

Therefore delta work=delta kinetic energy=416.16 J

Therefore Power= 416.16/ 2 s = 208.08 W.

Apparently the answer is just 416.16 J. When I use the second equation of P= F*v=102*4.08=416 J, I get the correct answer. Why are these two equations giving me different answers?

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# Homework Help: Sprinter Work and Power

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