Question

The engine of a motorcycle can produce a maximum acceleration$5m/s^2$ . Its brakes can produce a maximum retardation$10m/s^2$. 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

The correct option is A 30 sec

If a body starts from rest with acceleration $\alpha$and then retards with retardation$\beta$and becomes to rest.The total time taken for this journey is t and distance covered is S then

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

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