A red car is stopped at a traffic light waiting for it to turn green. Meanwhile,

Question

A red car is stopped at a traffic light waiting for it to turn green. Meanwhile, a blue car moving at 15 m/s is approaching the same stop light. When the blue car is still 20 m away from the light, it turns green, and both cars accelerate, the red one at 6 m/s2, the blue one at 2 m/s2.
(a) How far apart are the two cars after 1 s?
(b) How far has the red car traveled when the blue car passes it?
(c) Can the red car eventually overtake the blue car again without exceeding the speed limit of 30 m/s?

Explanation / Answer

(a) distance travelled by blue car = 15 + 2/2 = 16m
distance travelled by red car = 6 / 2 = 3m
distance between two cars after 1s = initial seperation + 3 -16
= 20+3-16 = 7m

(b) 15t +t2 -20 = 3t2

2t2 +15t -20 = 0

t = 1.155 s

distance travelled by red car = 3t2 = 3 x 1.552 = 7.21 m

(c) no it cannot overtake without exceeding 30m/s speed limit

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