Question

A car is moving along a straight horizontal road with a speed $v _ { 0 }$ . If the coefficient of friction between the tyres and the road is $\mu$ , the shortest distance in which the car can be stopped is

• A. $\frac { v _ { 0 } ^ { 2 } } { 2 \mu g }$
• B. $\frac { v _ { 0 } } { \mu g }$
• C. $\left( \frac { v _ { 0 } } { \mu g } \right) ^ { 2 }$
• D. $\frac { v _ { 0 } } { \mu }$

Answer 1

Answer: (A)

$\frac { v _ { 0 } ^ { 2 } } { 2 \mu g }$

Answer 2

Retarding force $F = m a = \mu R = \mu m g$

$\therefore$ $a = \mu g$

Now from equation of motion

$v ^ { 2 } = u ^ { 2 } - 2 a s$

$\Rightarrow 0 = u ^ { 2 } - 2 a s$ ⇒ $s = \frac { u ^ { 2 } } { 2 a } = \frac { u ^ { 2 } } { 2 \mu g }$ $\therefore$ $= \frac { v _ { 0 } ^ { 2 } } { 2 \mu g }$