The dirver of a car travelling at a velcituy (v) suddenly sees a broad wall in front of mim at a distance `r`. Is it better to brake or to turn sharply ?`

Explanation

It is better to apply brake than to turn sharply for the reason discussed below.
Let (m) be the be the mass of the car . When the driver applies the brakes, let the car stop at distance (x). Then retardation , ` a= v^(2) //2 x`
Retarding force, `F=ma =(mu)^(2)/2_(x) or x=(m v^(2) (2 F)`
There will be no collision if `x-ltr`
or ` ( mv)^(2) /(2 F) -lt r or F gt- (m v^(2)/(2 r)` ..(i)
If the driver takes a sharp turn of radius ` x`, then cretripetal force on car is,
` F' =(m v^(2))/x or x=(m v^(2))/ F'`
To avoid collision, `x -lt r ` so
` (m v^(2))/F' -ltr or F' gt- ( m v^(2))/r ` ...(ii)
From (i) and (ii) we note that ` F=F'//2`
It means to avoid collision braking force required is half the centripetal force. Therefore, braking is better.