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
Medium
Download our app for free and get started
(a) Retarding force $F = ma = \mu \,R = \mu \;mg$
$\therefore a = \mu g$
Now from equation of motion ${v^2} = {u^2} - 2as$
$ \Rightarrow \;0 = {u^2} - 2as$
$⇒$ $s = \frac{{{u^2}}}{{2a}} = \frac{{{u^2}}}{{2\mu \;g}}$
$\therefore s= \frac{{v_0^2}}{{2\mu \,g}}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two particles of equal masses are revolving in circular paths of radii ${r_1}$ and ${r_2}$ respectively with the same speed. The ratio of their centripetal forces isView Solution
- 2In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$View Solution
- 3A body of weight $64\, N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively, the acceleration of the body will be (Acceleration due to gravity $= g$)View Solution
- 4Consider a car moving on a straight road with a speed of $100\, m/s$. The distance at which car can be stopped, is ........ $m$. $[\mu_k = 0.5]$View Solution
- 5$A$ particle inside the rough surface of $a$ rotating cone about its axis is at rest relative to it at $a$ height of $1m$ above its vertex. Friction coefficient is $\mu = 0.5$, if half angle of cone is $45^o$, the maximum angular velocity of revolution of cone can be :View Solution
- 6A lift is moving downwards with an acceleration equal to acceleration due to gravity. A body of mass $m$ kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\,\mu $, then the frictional resistance offered by the body isView Solution
- 7A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $( N )$ and speed of the block $(v)$ ?View Solution
- 8The time taken by an object to slide down $45^{\circ}$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45^{\circ}$ incline plane. The coefficient of kinetic friction between the object and the incline plane isView Solution
- 9If mass of $A = 10\,\,kg$, coefficient of static friction $= 0.2$, coefficient of kinetic friction = $0.2$. Then mass of $B$ to start motion isView Solution
- 10Consider a block kept on an inclined plane (inclined at $45^{\circ}$ ) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane $(\mu)$ is equal toView Solution
