Two cars $A$ and $B$ are travelling in the same direction with velocities $v_{A}\ $and $v_{B}(v_{A} v_{B})$. When the car $A$ is at a distance $s$ behind car $B$, the driver of the car $A$ applies the brakes producing a uniform retardation $a$, there will be no collision when

Question

Two cars $A$ and $B$ are travelling in the same direction with velocities $v_{A}\ $and $v_{B}(v_{A} > v_{B})$. When the car $A$ is at a distance $s$ behind car $B$, the driver of the car $A$ applies the brakes producing a uniform retardation $a$, there will be no collision when

Dr. Abubacker · Accepted Answer

(c) For no collision, the speed of car $A$ should be reduced to $v_{B}$ before the cars meet, $ie,\ $final relative velocity of car $A$ with respect to car $B$ is zero $ie$, $v_{r} = 0$
Here initial relative velocity, $u_{r} = v_{A} - v_{B}$
Relative acceleration, $a_{r} = - a - 0 = - a$
Let relative displacement $= s_{r}$
The equation
$v_{r}^{2} = u_{r}^{2} + 2a_{r}s_{r}$
$(0)^{2} = \left( v_{A} - v_{B} \right) - 2as,$
$s_{r} = \frac{\left( v_{A} - v_{B} \right)^{2}}{2a}$
For no collision, $s_{r} \leq s$
$ie,\ \frac{\left( v_{A} - v_{B} \right)^{\ }}{2a} \leq s$

Q. Two cars $A$ and $B$ are travelling in the same direction with velocities $v_{A}\ $and $v_{B}(v_{A} > v_{B})$. When the car $A$ is at a distance $s$ behind car $B$, the driver of the car $A$ applies the brakes producing a uniform retardation $a$, there will be no collision when

Explanation

Reviewed by Dr. Abubacker

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