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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?

Respuesta :

Answer:

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

Explanation:

Initially the relative speed of the two cars is given as

[tex]v_r = v_b - v_w[/tex]

[tex]v_r = 2v_o - v_o = v_o[/tex]

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

[tex]a_r = -a_b[/tex]

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

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]0 - v_o^2 = 2(-a_b)d[/tex]

[tex]d = \frac{v_o^2}{2a_b}[/tex]

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

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