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

Answer: (C)

$\sqrt{a_{w}\, a_{r}}$

Answer 2

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 $t \approx t_r$
$\frac{v^2}{t^2} = a_w \cdot a_r$
$\frac{v}{t} = \sqrt{a_w \cdot a_r}$