posted by george .
A person driving her car at 56km/hr approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 20.s before turning to red, and she is 30m away from the near side of the intersection. The intersection is 15m wide. Her car's maximum deceleration is -6.2m/s^2, whereas it can accelerate from 56km/hr to 70km/hr in 4.2s. Ignore the length of her car and her reaction time.
a.) if she hits the brakes, how far will she travel before stopping?
b.) if she hits the gas instead, how far will she travel before the light turns red?
c.) should she try to stop or should she speed up to cross the intersection before the light turns red?
x = x0 + v0*t + 1/2*a*t^2
v = v0 + a*t
where x is position, x0 is initial position, v0 is initial speed, a is acceleration/deceleration, t is time, and v is speed as a function of time
a) 56 - 6.2*t^2 = 0
Solve for t, the time it takes for the speed to go to zero. The distance traveled in this time is then 1/2*6.2*t^2
b) 56 + a*4.2 = 70
Solve for a, the acceleration
Then calculated the distance she travels (I would assume that she stops accelerating after she hits 70 km/hr
So for the first 4.2 seconds, she travels
x1 = 56*t + 1/2*a*4.2^2
and then she travels an additional distance:
x2 = 70*(20-4.2)
for a total distance of x1 + x2
c) Evaluate where she will be in part a) and b) with respect to the traffic lights and decide what she should do