Question

Two cars are in a race. The white car passed the finishing point with a velocity $ v\, ms^{-1} $ more and took time $ t\, s $ less than the red car. If both the cars start from rest and travel with constant accelerations $ a_w $ , and $ a_r $ respectively, $ \frac{v}{t} $ is given

• A. $ a_w\, a_r $
• B. $ \sqrt{\frac{a_{w}}{a_{r}}} $
• C. $ \sqrt{a_{w}\, a_{r}} $
• D. $ \sqrt{\frac{a_{r}}{a_{w}}} $

Answer 1

The Correct Option is C

We have, $v = u + at$
For White car, $v = a_w t $
$\Rightarrow \frac{v}{t} = a_w \,\,\,\,\,\,[u = 0 ] ...(i)$
For red car, $v_R = a_r t_r \,\,\frac{v_r}{t_r} = a_r \,\,\,\,\,...(ii)$
So, $\frac{v}{t} \cdot \frac{v_r}{t_r} = a_w \cdot a_r$
Suppose $ v \approx v_R $ and $ t \approx t_r$
$\frac{v^2}{t^2} = a_w \cdot a_r$
$\frac{v}{t} = \sqrt{a_w \cdot a_r}$