Q. The engine of motorcycle can produce a maximum acceleration $5\ m/s^{2}$. Its brakes can produce a maximum retardation $10\ m/s^{2}$. What is the minimum time in which it can over a distance of $1.5\ km$
A) $30\ sec$
B) $15\ sec$
C) $10\ sec$
D) $5\ sec$
Explanation
(a) If a body starts from rest with acceleration $\alpha$ and then retards with retardation $\beta$ and comes to rest. The total time taken for this journey is $t$ and distance covered is $S$
$Then\ S = \frac{1}{2}\frac{\alpha\beta t^{2}}{(\alpha + \beta)} = \frac{1}{2}\frac{5 \times 10}{(5 + 10)} \times t^{2}$
$\Rightarrow 1500 = \frac{1}{2}\frac{5 \times 10}{(5 + 10)} \times t^{2} \Rightarrow t = 30\ sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.