A person driving her car at 60 km/h approaches an intersection just as the traff

Question

A person driving her car at 60 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection. The intersection is 15 m wide. Her car's maximum deceleration is -6.2 m/s2, whereas it can accelerate from 60 km/h to 70 km/h in 3.0 s. Ignore the length of her car and her reaction time.

If she hits the brakes, how far will she travel before stopping?
m
If she hits the gas instead, how far will she travel before the light turns red?
m
Should she try to stop, or should she speed up to cross the intersection before the light turns red?

stopspeed up   

Explanation / Answer

60 km/h = 16.6667 m/s

to find the breaking distance use
v^2 = v0^2 + 2as with v = 0, s = 30 m, and a = - 6.2 m/s^2.
0 = 16.6667^2 - 2*6.2*s
s = 22.40 m

find the acceleration:
v = v0 + at
70/3.6 = 60/3.6 + a*3.0

19.444 = 16.666 + 3.0a

2.778 = 3.0a
a = 0.926 m/s^2

you can find the distance she can go in 2 seconds by
s = v0*t + 1/2*at^2
s = 16.667*2 + 1/2*0.926*2^2
s = 35.186 m

So she will not make it across the street in 2 seconds.
She better brakes.

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