Question

A car starts from rest on a 1600 m long bridge. The coefficient of friction between the tyre and road is 0.8. The minimum time taken by the car to cross the bridge is

Answer 1

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Answer 2

Answer:

The minimum time taken by the car to cross the bridge is $20 sec$

Explanation:

Let a maximum acceleration is produced in car.

$m a=\mu R$

(For more accelerations the tyres will slip]

$\begin{aligned}&\Rightarrow \mathrm{ma}=\mu \mathrm{mg} \\&\Rightarrow \mathrm{a}=\mu \mathrm{g}=1 \times 10=10 \mathrm{~m} / \mathrm{s}^{2}\end{aligned}$

For the crossing of the bridge in minimum time, it has to travel with maximum acceleration.

$\mathrm{u}=\mathrm{0}, \mathrm{s}=1600, \mathrm{a}=0.8 \mathrm{~m} / \mathrm{s}$

From s $=u t+\frac{1}{2} a t^{2}$

$\begin{aligned}&1600=0+\left(\frac{1}{2}\right) 0.8 t^{2} \\&\Rightarrow t=\sqrt{400}=20 \text { sec }\end{aligned}$