Two cars A and B are travelling in the same direction with velocities $v_{1}$ and $v_{2} (v_{1} > v_{2})$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake 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_{1}

and

v_{2} (v_{1} > v_{2})

When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

Toppr Admin · Accepted Answer

Initial relative velocity vA-x2212-vB- is reduced to 0 in distance d-x2032-lt-d- with retardation a-x2234-02-x2212-vA-x2212-vB-2-2ad-x2032-x2234-d-x2032-vA-x2212-vB-22a-x2234-d-gt-vA-x2212-vB-22a

Two cars A and B are travelling in the same direction with velocities vA and vB(vA>vB). When the car A is at a distance d behind the car B the driver of the car A applies brakes producing a uniform retardation a. There will be no collision whend<(vA−vB)22ad<v2A−v2B2ad>(vA−vB)22ad>v2A−v2B2a

Initial relative velocity vA−vB, is reduced to 0 in distance d′(<d) with retardation a.∴02−(vA−vB)2=2ad′∴d′=(vA−vB)22a∴d>(vA−vB)22a

Initial relative velocity $v_{A} - v_{B}$ , is reduced to $0$ in distance $d^{'} (< d)$ with retardation $a$ .
$∴ 0^{2} - {(v_{A} - v_{B})}_{A}^{2} = 2 a d^{'}$
$∴ d^{'} = \frac{{(v_{A} - v_{B})}_{A}^{2}}{2 a}$
$∴ d > \frac{{(v_{A} - v_{B})}_{A}^{2}}{2 a}$