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Grade 11Mechanics

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.

MANOJ

12 Years agoGrade 11

1 Answer

Sumit Majumdar

12 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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