Net External Force on a Sprinter| Newton’s Second Law of Motion: Concept of a System| Dynamics| College Physics| Problem 4.2

If the sprinter from the previous problem accelerates at that rate for 20 m, and then maintains that velocity for the remainder of the 100-m dash, what will be his time for the race?

SOLUTION:

For the first segment of the sprint, we are given m=63.0\:kg, a=4.20\:m/s^2, and v_o=0\:m/s, The final velocity for this segment is

v^2=\left(v_o\right)^2+2ax

v^2=0+2\left(4.20\:m/s^2\right)\left(20\:m\right)

v=\sqrt{168}

v=12.961\:m/s

Given the final velocity after running for 20 meters, we can find the time it took him to do so.

t=\frac{v-v_o}{a}

t=\frac{12.961\:m/s-0\:m/s}{4.20\:m/s^2}

t=3.086\:s

For the second segment of the sprint, we know that a=0\:m/s^2;\:v=12.961\:m/s,\:x=80\:m. We are going to solve for the time the sprinter took to run this segment. 

t=\frac{d}{v}

t=\frac{80\:m}{12.961\:m/s}

t=6.172\:s

Therefore, the total time it took the sprinter to run the whole 100-m dash is

Total\:time=3.086\:s+6.172\:s

Total\:time=9.258\:s