Answer
10.18 s
Work Step by Step
As the acceleration is constant, the time taken by the sprinter to reach his top speed is obtained using the relation
$x-x_{0}=\frac{1}{2}(v_{0}+v)t$
where $x-x_{0}=12.0\,m$ and $v_{0}+v=(0+11.0)m/s$
$\implies t=\frac{12.0\,m}{11.0\,m/s}\times2=2.18\,s$
As the speed is constant, the remaining time to complete the 100 m race is obtained using the relation:
$Time\,interval=\frac{distance}{speed}=\frac{(100-12)m}{11.0\,m/s}=8.00\,s$
Total time for the 100 m race= $2.18\,s+8.00\,s=10.18\,s$.
