Question

Consider a car moving on a straight road with a speed of \[100m/s\] . The distance at which a car can be stopped \[\left( {{\mu _k} = 0.5} \right)\]
A. \[100m\]
B. \[400m\]
C. \[800m\]
D. \[1000m\]

Answer 1

Hint: To find the distance at which the car stops, first we must find the acceleration of the car when the brakes are applied. Once we find the acceleration we need to find the distance necessary to stop the car if the acceleration or retardation is split. The expression used is:
${v^2} = {u^2} + 2aS$ here$v$ is the final velocity, $u$ is the initial velocity, \[a\] is the acceleration, and \[S\] is the distance at which it is made still.

Complete step by step solution:
The speed by which the car is moving is known as velocity$u$. Now, the car is stationary due to the use of the brakes which makes the final velocity zero. Therefore, the distance to stop is $d$ and the initial velocity is \[u\] , in turn, makes the acceleration of the car till stop as $a$, and to estimate the value of we apply the relation of ${v^2} = {u^2} + 2aS$. Once we get the acceleration value, we substitute the value of the acceleration in the second case or when the car comes to a stop. In the question when the car is stopped by friction, the initial velocity $u = 100m/s$, the given coefficient ${\mu _k} = 0.5$ , and $g = 10m/{s^2}$ .
The retarding force is given as $ma = \mu R$
\[ma = \mu mg\] Which becomes \[a = \mu g\]
Let the car cover distance $S$with velocity $u$ and stop. Hence we know that the relation for finding the stopping distance is given by
${v^2} = {u^2} + 2aS$
$ \Rightarrow {v^2} - {100^2} = 2aS$
$ \Rightarrow {u^2} = 2aS$as$v = 0$
$ \Rightarrow S = \dfrac{{{u^2}}}{{2a}} = \dfrac{{{{100}^2}}}{{2 \times \mu g}} = \dfrac{{{{100}^2}}}{{2 \times 0.5 \times 10}}$
Therefore the stopping distance is \[S = 1000m\]

Note:
The word retardation means backward or negative acceleration where the acceleration is applied during braking purposes. Thus the stopping distance can be defined as the distance covered by the body before it rests. It is related to various factors like road surfaces, the reflex of the driver, etc. Its SI unit is meter\[m\].