- #1

cmkluza

- 118

- 1

## Homework Statement

A 49.0 kg sprinter, starting from rest, runs 58.0 m in 9.90 s at constant acceleration.

What is the sprinter's power output at 1.90 s , 3.00 s , and 5.70 s ?

## Homework Equations

##d=v_it + \frac{1}{2}at^2##

##F=ma##

##W=Fd##

##P=\frac{W}{t}##

## The Attempt at a Solution

I got the acceleration from given data:

##58=(0)(9.9) + \frac{1}{2}(a)(9.9)^2 \longrightarrow a \approx 1.184 m/s^2##

Then I got the force:

##F=(49)(1.184) \approx 58 N##

Then I tried to calculate the distance traveled at different time intervals, starting with at ##t=1.90##:

##d=\frac{1}{2}(1.184)(1.9)^2 \approx 2.14##

Finally, I tried to get Work and then Power from that:

##W=Fd=(58)(2.14)=123.9 J \longrightarrow P=\frac{W}{s}=\frac{123.9}{1.9} \approx 65.2 W##

However, this is not correct, the correct answer is 130 W. What am I doing wrong here?