Answer:
The time for the entire race is 11.39 sec.
Explanation:
Given that,
Distance = 15 m
Remainder distance = 100 m
Suppose A sprinter begins a race with an acceleration of 3.4 m/s².
We need to calculate the time
Using equation of motion
![s=ut+\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
Put the value in the equation
![15=0+\dfrac{1}{2}\times3.4\times t^2](https://tex.z-dn.net/?f=15%3D0%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes3.4%5Ctimes%20t%5E2)
![t^2=\dfrac{30}{3.4}](https://tex.z-dn.net/?f=t%5E2%3D%5Cdfrac%7B30%7D%7B3.4%7D)
![t=2.97\ sec](https://tex.z-dn.net/?f=t%3D2.97%5C%20sec)
We need to calculate the final velocity of sprinter
Using equation of motion again
![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
Put the value into the formula
![v=0+3.4\times2.97](https://tex.z-dn.net/?f=v%3D0%2B3.4%5Ctimes2.97)
![v=10.09\ m/s](https://tex.z-dn.net/?f=v%3D10.09%5C%20m%2Fs)
We need to calculate the distance covers by sprinter
![d=100-15=85\ m](https://tex.z-dn.net/?f=d%3D100-15%3D85%5C%20m)
The sprinter need to covers only 85 m.
We need to calculate the time
Using formula of time
![t=\dfrac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bd%7D%7Bv%7D)
Put the value into the formula
![t'=\dfrac{85}{10.09}](https://tex.z-dn.net/?f=t%27%3D%5Cdfrac%7B85%7D%7B10.09%7D)
![t'=8.42\ sec](https://tex.z-dn.net/?f=t%27%3D8.42%5C%20sec)
We need to calculate the time for the entire race
![t''=t+t'](https://tex.z-dn.net/?f=t%27%27%3Dt%2Bt%27)
Put the value into the formula
![t''=2.97+8.42](https://tex.z-dn.net/?f=t%27%27%3D2.97%2B8.42)
![t''=11.39\ sec](https://tex.z-dn.net/?f=t%27%27%3D11.39%5C%20sec)
Hence, The time for the entire race is 11.39 sec.