Question

A white car is traveling at the legal speed limit v0 along an interstate highway. A blue car traveling in the same direction at twice the legal limit draws alongside the white car and (mistakenly) thinks it is a police car. The blue car slows down with constant acceleration a = −ab and the white car continues at its previous constant speed. How far apart are the cars when the blue car’s speed is the legal speed limit?

Answer 1

Answer:

the distance between two cars becomes $d = \frac{v_o^2}{2a_b}$ when blue car travels at legal speed

Explanation:

Initially the relative speed of the two cars is given as

$v_r = v_b - v_w$

$v_r = 2v_o - v_o = v_o$

now the relative acceleration of blue car with respect to white car

$a_r = -a_b$

now the distance between two cars till the relative speed of two cars comes to zero

$v_f^2 - v_i^2 = 2 a d$

$0 - v_o^2 = 2(-a_b)d$

$d = \frac{v_o^2}{2a_b}$

so the distance between two cars becomes $d = \frac{v_o^2}{2a_b}$ when blue car travels at legal speed