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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.

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.
 

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 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

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