Question

The engine of a motorcycle can produce a maximum acceleration 5 m/s². Its brakes can produce a maximum retardation 10 m/s². What is the minimum time in which it can cover a distance of 1.5 km

• A. 30 sec
• B. 15 sec
• C. 10 sec
• D. 5 sec

Answer 1

Answer: (A)

30 sec

Answer 2

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

$S = \frac{1}{2}\frac{\alpha\beta t^{2}}{(\alpha + \beta)} = \frac{1}{2}\frac{5 \times 10}{(5 + 10)} \times t^{2}$

⇒ $1500 = \frac{1}{2}\frac{5 \times 10}{(5 + 10)} \times t^{2}$ $\Rightarrow \mspace{6mu}\mspace{6mu} t = 30\sec$.