Question

You are driving a car at the 25-mi/h speed limit when you observe the light at the intersection 65 m in front of you turn yellow. You know that at that particular intersection the light remains yellow for exactly 6.0s before turning red. After you think for 1.0 s, you then accelerate the car at a constant rate. You somehow manage to pass your 4.1 m car completely through the 15.0 m wide intersection just as the light turns red, thus narrowly avoiding a ticket for running a red light. Immediately after passing through the intersection you take your foot off the accelerator, relieved. However, down the road you are pulled over for speeding. You assume you were ticketed for the speed of your car as it exited the intersection. Determine this speed and decide whether you should fight this ticket in court.

Answer 1

`v_f = 50 mph`

since the speed is exceeded the speed limit so it should not cross the junction

Step-by-step explanation:

Initial speed of the car is given as

`v_i = 25 mph`

now we will have

`v_i = 11.2 m/s`

now the distance that car should move to cross the intersection is given as

`d = 65 + 15 + 4.1`

`d = 84.1 m`

Now time to cross the junction is

`t = 6 - 1 = 5 s`

now the acceleration of the car must be

`d = v_i t + (1)/(2)at^2`

`84.1 = 11.2(5) + (1)/(2)a(5^2)`

`a = 2.25 m/s^2`

Now the final speed of the car is given as

`v_f = v_i + at`

`v_f = 11.2 + (2.25* 5)`

`v_f = 22.4 m/s`

`v_f = 50 mph`

since the speed is exceeded the speed limit so it should not cross the junction