Two cars A and B are moving in the same direction with veloc... | PHYSICS - RELATIVE MOTION | SolveeIt

Question

Two cars A and B are moving in the same direction with velocities 50 m/s and 30 m/s. When car A is at a distance d behind car B, the driver of car A applies the brake producing a uniform retardation of 4 m/s². There will be no collision when:

$d < 25$ m

$d > 25$ m

$d < 50$ m

$d > 50$ m

Answer

$d > 50$ m

Explanation

Solution

The initial relative velocity of car A with respect to car B is $u_{rel} = v_A - v_B = 50 \text{ m/s} - 30 \text{ m/s} = 20 \text{ m/s}$ . The relative acceleration of car A with respect to car B is $a_{rel} = a_A - a_B = -4 \text{ m/s}^2 - 0 = -4 \text{ m/s}^2$ . The relative stopping distance $s_{rel}$ is the distance A travels relative to B before stopping. Using $v_{rel}^2 = u_{rel}^2 + 2a_{rel}s_{rel}$ with $v_{rel} = 0$ : $0^2 = (20)^2 + 2(-4)s_{rel}$ $0 = 400 - 8s_{rel} \implies s_{rel} = 50 \text{ m}$ . For no collision, the initial distance $d$ must be greater than the relative stopping distance $s_{rel}$ . Thus, $d > 50 \text{ m}$ .

Question: Two cars A and B are moving in the same direction with velocities 50 m/s and 30 m/s. When car A is ...

Solution