7 You were waiting in a standing still queue in front of a t

7. You were waiting in a standing still queue in front of a traffic light on a street with a 30-mph speed limit. When the light turns green, you counted, and it took 20 seconds for the first vehicle in the upcoming direction to pass you (assuming that vehicles are taking 10 ft/s2 acceleration when speeding up). It took another 20 seconds for you to start moving. -How far are you from the intersection? What is the speed of the shockwave caused by the green light? If the v-k function is v=601-0.5k), how long will it take you to pass the start bar after you start moving?

Solution

It took 20 seconds for a vehicle from standing still to speed up with an acceleration of 10ft/s2 and cross my vehicle which is at some distance from the intersection (lets say distance D)

initial velocity of upcoming vehicle = u = 0 (it was standing when the signal wasn\'t green)

accelaration = a1= 0 ft/s2

time taken 20 seconds

distance travelled by the upcoming vehiclecan be calculated by using the relation -

D = ut+1/2at²

D = 0 + 1/2 x 10 x 20² = 2000 ft (approx 610 metres)

When green light is on,

speed of shockwave can be found out by using distance = 2000 ft, u = 0 and a = 10 ft/s2

v² = u² + 2xaxd

v² = 0 + 2 x 20 x 2000

v = 28.28 ft/sec