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

the distance between two cars becomes
`d = (v_o^2)/(2a_b)` when blue car travels at legal speed

Step-by-step 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 = (v_o^2)/(2a_b)`

so the distance between two cars becomes
`d = (v_o^2)/(2a_b)` when blue car travels at legal speed