The driver of a car travelling with velocity `v` on a road suddenly sees a broad wall in front of him at a distance `r`. He has two alternatives: to turn sharply or a brake instantly. The passenger who is a professor of physics, advises him to brake to avoid collision.
Read the above passage and answer the following questions:
(i) How is the suggestion from Professor of Physics justified?
(ii)Does the suggestion work really?
(iii)What value do you learn from this experience?

Explanation

(i)When the car of mass `m` stops at distance `x`, retardation produced, `a=v^(2)//2 x`.
Retarding force `F= ma= (mv^(2))/(2x)` or `x=(mv^(2))/(2F)`
There will be no collision, If `x lt r` or `(mv_(2))/F'` or `Fge (mv^(2))/(2r)`
If the driver takes a sharp turn of radius `x`, then centripetal force on car is `F'= (mv^(2))/x` or `x=(mv^(2))/F'`
To avoid collision, `x gt = r`, so that `(mv^(2))/F'ger` or `F'ge(mv^(2))/r`
Clearly, `F=F//2` i.e., braking force required is only half the (centripetal) force required for a sharp turn.
Hence, the suggestion is justified.
(i)Yes, the suggestion works and the collision is saved.
(iii)We learn that we should drive carefully at reasonalbe speed and in case of emergency, we should not hesitate to consult the co-passenger.