Question

A sprinter runs a $100m$ race in a straight line. He accelerates from the starting block at constant acceleration of $2.5{ms}^{-1}$ to reach his maximum speed of $10{ms}^{-1}$. He maintains this speed until he crosses the finish line.

Which time does it take the sprinter to run the race?

• A. $4s$
• B. $10s$
• C. $12s$
• D. $20s$

Answer 1

The correct option is C $12s$

The time taken to reach max. speed = $\frac{v-u}{a}$

= $\frac{(10-0)m{s}^{-1}}{2.5m{s}^{-2}}$

=$4s$

So, total distance covered in this $4s$ = $\frac{1}{2}a{t}^2$

= $\frac{1}{2}\times 2.5\times 4^2$

= $20m$

Time taken to complete rest $(100-20)m$= $\frac{(100-20)m}{10m{s}^{-1}}$

=$8s$

So, total time taken = $(8+4)s=12s$