Question

The engine of a futuristic nuclear-powered car for which power and speed can have fantastic values kph) can produce a maximum acceleration of 5$m/s^2$ and its brakes can produce a maximum retardation of10$m/s^2$ . The minimum time in which a person can reach his workplace, located 1.5$km$ away from his home using this car is

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

Answer 1

The correct option is D 30$sec$

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$,$

$S=\frac{1}{2}\frac{\alpha \beta t^2}{\left(\alpha +\beta \right)}$

$=\frac{1}{2}\frac{5\times 10}{\left(5+10\right)}\times t^2$

$\Rightarrow 1500=\frac{1}{2}\frac{5\times 10}{\left(5+10\right)}\times t^2$

$\Rightarrow t=30\sec$

Hence,

option $\left(D\right)$ is correct answer.