(adsbygoogle = window.adsbygoogle || []).push({}); As soon as a traffic light turns green, a car speeds up from rest to 50.0 mi/h with constant acceleration 9.00 mi/h/s. In the adjoining bicycle lane, a cyclist speeds up from rest to 20.0 mi/h with constant acceleration 13.0 mi/h/s. Each vehicle maintains constant velocity after reaching its cruising speed. (a) For what time interval is the bicycle ahead of the car? (b) By what maximum distance does the bicycle lead the car?

after conversion of units to m/s:

car a=4.022, v=22.35

bike a =5.81, v = 8.94

car reaches max v in 22.35/4.022 = 5.56 s

car displacement (if t < 5.56) is 0.5a_{car}t^{2}, and (t > 5.56) 0.5a_{car}(5.56)^{2}+ 22.35(t-5.56)

bike reaches max v in 8.94/5.81 = 1.54 s

bike displacement (if t < 1.54) is 0.5a_{bike}t^{2}, and (t > 1.54) 0.5a_{bike}(1.54)^{2}+ 8.94(t-1.54)

at t=1.54, bike is ahead of car

at t=5.56, car is ahead of bike

so for part a) i know 1.54 < t < 5.56

so equation is 0.5a_{car}t^{2}= 0.5a_{bike}(1.54)_{2}+ 8.94(t-1.54)

solving, t = 3.45 s

my question is how to get part B?From a prev question, they said something about setting the velocity equal.

so I set bike 8.94 = a_{car}t

t = 2.22

putting it in car equation x = 9.91, and bike equation x = 12.97

So their greatest separation would be about 3.06 m. IS THIS CORRECT? I don't have an answer key and someone else's solution does not match mine.

thanks!

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# Car vs bike (acc to const)

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