College Physics 4.2 – The time for the race of a sprinter subjected to a force

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?


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





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




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




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

\text{Total time}=3.086\:\text{s}+6.172\:\text{s}

\text{Total time}=9.258\:\text{s}