Question

A person moves along a circular thread with speed $10m{s}^{-1}$. He covers one cycle in $10minutes$. The person is now challenged to complete it in half the time. What should be the constant acceleration that the person should maintain to complete his challenge? Assume he is starting from rest.

• A. $\frac{1}{15}$ $m{s}^{-2}$
• B. $\frac{2}{15}$ $m{s}^{-2}$
• C. $\frac{2}{13}$ $m{s}^{-2}$
• D. $\frac{4}{13}$ $m{s}^{-2}$

Answer 1

The correct option is B $\frac{2}{15}$ $m{s}^{-2}$

Given,
speed $=10m{s}^{-1}$ and
time taken = 10 minutes $=10\times 60=600s$

So, length of thread = $speed\times time$ = $10\times 600=6000m$

Now the person A has to cover distance $6000m$ in half the time, i.e. $5minutes$ . He will start from rest, so initial velocity will be zero $u=0m{s}^{-1}$.
Using second equation of motion, $s=ut+\frac{1}{2}a{t}^2$
$6000=0+\frac{1}{2}\times a\times (60\times 5{)}^2$
On solving we get, $a=\frac{6000}{45000}=\frac{2}{15}m{s}^{-2}$