Two cars $A$ and $B$ are travelling in the same direction with velocities ${v_1}$ and ${v_2}$$({v_1} > {v_2})$. When the car $A$ is at a distance $d$ ahead of the car $B$, the driver of the car $A$ applied the brake producing a uniform retardation $a$ There will be no collision when
Two cars $A$ and $B$ are travelling in the same direction with velocities ${v_1}$ and ${v_2}$$({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
$d < \frac{{{{({v_1} - {v_2})}^2}}}{{2a}}$
$d < \frac{{v_1^2 - v_2^2}}{{2a}}$
$d > \frac{{{{({v_1} - {v_2})}^2}}}{{2a}}$
$d > \frac{{v_1^2 - v_2^2}}{{2a}}$
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
Initial relative velocity $ = {v_1} - {v_2}$, Final relative velocity $ = 0$
From ${v^2} = {u^2} - 2$ as $ ⇒ 0 = {({v_1} - {v_2})^2} - 2 \times a \times s$
$⇒ s = \frac{{{{({v_1} - {v_2})}^2}}}{{2a}}$
If the distance between two cars is $'s'$ then collision will take place. To avoid collision $d > s$
$\therefore d > \frac{{{{({v_1} - {v_2})}^2}}}{{2a}}$
where $d = $ actual initial distance between two cars.