What is stopping distance for vehicle ? What will be the stopping distance if the initial velocity is doubled ?
What is stopping distance for vehicle ? What will be the stopping distance if the initial velocity is doubled ?
When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance.
Suppose, the velocity of moving vehicle is $v_{0}$. After applying brakes retardation : $-a$
Distance covered : $d_{\mathrm{s}}$ (stopping distance)
Final velocity : $v=0$
In equation $v^{2}-v_{0}^{2}=2 a x$
$\therefore 0-v_{0}^{2}=2(-a)\left(d_{\mathrm{s}}\right)\left(\because v=0, a=-a, s=d_{\mathrm{s}}\right)$
$\therefore v_{0}^{2}=2 a d_{\mathrm{s}}$
$\therefore d_{\mathrm{s}}=\frac{v_{0}^{2}}{2 a}$
Here, $a$ is value of retardation and it is constant.
Thus, stopping distance is proportional to square of the initial velocity.
$\therefore d_{\mathrm{s}} \propto v_{0}^{2}$
Stopping distance, $d_{\mathrm{s}} \propto v_{0}^{2}$
$\therefore \frac{(d \mathrm{~s})_{2}}{(d \mathrm{~s})_{1}}=\frac{\left(v_{0}\right)_{2}^{2}}{\left(v_{0}\right)_{1}^{2}}=(2)^{2}=4$
$\therefore$ Stopping distance becomes $4$ times.
Similar Questions
A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
- [IIT 1978]
Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be.........$m/{s^2}$
Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be.........$m/{s^2}$
A car is moving with speed of $150\,km / h$ and after applying the brake it will move $27\,m$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling $....m$ distance.
A car is moving with speed of $150\,km / h$ and after applying the brake it will move $27\,m$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling $....m$ distance.
- [JEE MAIN 2022]
Suggest a suitable physical situation for following graphs.
Suggest a suitable physical situation for following graphs.
A body starts from rest from the origin with an acceleration of $6\,m/{s^2}$ along the $x-$axis and $8\,m/{s^2}$ along the $y-$axis. Its distance from the origin after $4 \,seconds$ will be........$m$
A body starts from rest from the origin with an acceleration of $6\,m/{s^2}$ along the $x-$axis and $8\,m/{s^2}$ along the $y-$axis. Its distance from the origin after $4 \,seconds$ will be........$m$