Question

A person starts from rest on amotorcycle with acceleration $\alpha$ and then retards with retardation $\beta$ and comes to rest.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 regards with retardation $\beta$ and comes to rest.
The total time 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.