Question

A car driver going at some speed 'v' suddenly finds a wide wall at distance 'r'. Should he apply brakes or turn the car in a circle of radius 'r' to avoid hitting the wall ?

Answer 1

While moving in a car, If Car Drivers saw the wall at the distance of r then he need to turns the bike with some velocity such that Frictional Force can balances it otherwise car may collapsed with the wall.

Let us derive the mathematical expression for that.

     In case of the Motion around the cut,

          Friction ≥ mv²/r

⇒ μmg ≥ mv²/r

⇒ v ≤ √(μrg)

Means if the velocity of the car will be less than that of root of μrg then the drivers don't need to apply the brakes but if it is greater than that of this, then we must apply the brakes so to decelerates it and make it equal or less than the given value of velocity.

Hope it helps.

Answer 2

If the car's speed is smaller than that of the μrg root then the drivers don't have to apply the brakes, but if it's higher than that, then we have to apply the brakes to decelerate it and make it equivalent or lower than the speed value.  

Explanation:

Step 1:

When travelling in a car, if Car Drivers saw the wall at r distance, then it's necessary to turn the bike at some speed so that Frictional Force can balance it, otherwise the car will collapse with the wall.Let us derive the mathematical expression for that.

Step 2:

In the case of the cutting motion,

$\begin{equation}\begin{aligned}&\text {friction} \geq \frac{m v^{2}}{r}\\&\mu m g \geq \frac{m v^{2}}{r}\\&\mu m g r \geq m v^{2}\\&\mu r g \geq v^{2}\\&v \leq \sqrt{\mu r g}\end{aligned}$

Step 3:

Means if the car's speed is smaller than that of the μrg root then the drivers don't have to apply the brakes, but if it's higher than that, then we have to apply the brakes to decelerate it and make it equivalent or lower than the speed value.