Question

A car has a headlight which can illuminate a horizontal straight road in front upto a distance of $10\text{m}$. If the coefficient of friction between tyre and road is $0.5$, the maximum safe speed of the car during a night drive is
[Neglect the reaction time of the driver and take $g=10{\text{m/s}}^2$]

• A. $5\text{m/s}$
• B. $8\text{m/s}$
• C. $10\text{m/s}$
• D. $12\text{m/s}$

Answer 1

The correct option is C $10\text{m/s}$

Here, friction is acting between the tyre and the road. So, acceleration of car will be

$a=\frac{f}{m}=\frac{\mu mg}{m}=\mu g$

$a=0.5\times 10=5{\text{m/s}}^2$

For safe drive, car must stop within the maximum visible safe distance. So,

$s=10\text{m}$

Now applying equation of motion,

$v^2-u^2=2as$

Here, $v=0;a=-5{\text{m/s}}^2;s=10\text{m}$

$0^2-u^2=-2\times 5\times 10$

$\Rightarrow u=\sqrt{10\times 10}$

$\therefore u=10\text{m/s}$

Therefore, option $\left(c\right)$ is correct.
$$\begin{array}{c}\text{Why this question?}\\ \text{Concept- If speed is greater than maximum safe}\\ \text{speed then the car will not be able to stop before}\\ 10\text{m}\text{and there can be an accident.}\end{array}$$