Question

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

Answer 1

The force needed to apply brakes is just half of the force required to take the circular turn, it is better to apply brakes.

Explanation:

Let F1 be the braking force, so as to stop the car just in the distance r.  

Then,

Work done by the braking force = kinetic energy of the car

or F1 x r = 1/2 mv2

or F1 = (mv2) / 2r           -------(1)

Let F2 be th force required (centripetal force force) for taking a circular turn of radius r.

Then,

F2 = mv^2 / r     ------- (2)

From the equations (1) and (2), we have

F1 = 1/2 F2

Since the force needed to apply brakes is just half of the force required to take the circular turn, it is better to apply brakes.