# Mashood finishes a race t seconds before Ravi and has a finishing speed which is v m/s more than Ravi’s. Assuming both have uniformly accelerated from rest throughout the race, find the product of the accelerations of the two runners in SI units.

Sumit Majumdar IIT Delhi
8 years ago
Dear student,
Let us assume the distance between the starting and ending points be D and the time taken by Mashood be T sec.
So, we have the speeds of mashood and ravi are:
$u_{m}=\frac{d}{T}, u_{r}=\frac{d}{T+t}$
hence, the difference in speeds gives us:
$v=\frac{dt}{\left (T+t \right )T}\rightarrow d=\frac{v\left ( T+t \right )T}{t}$
now,
$\left (u_{m}-u_{r} \right )^{2}=u_{m}^{2}+u_{r}^{2}-2u_{m}u_{r}$
Also,$u_{m}^{2}=2a_{m}d, u_{r}^{2}=2a_{r}d$
Substituting for all values, we get:
$a_{m}a_{r}=\frac{v^{2}}{4t^{2}}$
Regards
Sumit