A person driving her car at 46.0 km/hr approaches an intersection just as the tr

Question

A person driving her car at 46.0 km/hr approaches an intersection just as the traffic light turns yellow (see figure below). She knows that the yellow light lasts only 1.60 s before turning to red, and she is a distance D = 30.0 m away from the near side of the intersection. If she decides to stop, how far from the intersection will she come to a stop? The intersection is W =17.0 m wide. Her car's maximum deceleration is -5.90 m/s2. Ignore the length of her car and her reaction time. Assume the beginning of the intersection the origin of your x-coordinate and take distances beyond the intersection to be positive and distances before the intersection to be negative.

Part B

The car can accelerate from 46.0 km/hr to 71.0 km/hr in 6.20 s. How far from the intersection will she be when the light turns red?

Explanation / Answer

A) initial speed of car , u = 46 km/h

u = 12.8 m/s

acceleration, a = -5.90 m/s^2

Now, using third equation of motion

v^2 - u^2 = 2 * a * d

0 - 12.8^2 = 2 * (-5.90) * d

d = 13.9 m

distance from the intersection = -(30 - 13.9)

distance from the intersection = -16.1 m

the distance from the intersection is -16.1 m

B)

v = 71 km/h

v = 19.7 m/s

acceleration , a = (19.7 - 12.8)/6.20

a = 1.12 m/s^2

Now, using second equation of moiton

d = 12.8 * 1.5 + 0.5 * 1.12 * 1.5^2

d = 20.46 m

distance from intersection = -(30 - 20.46)

distance from intersection = -9.54 m

the distance from intersection is -9.54 m

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