Question

At the instant a traffic light turns green, a car that has been waiting at the intersection starts ahead with a constant acceleration of 2.00 m/s2 . At that moment a truck traveling with a constant velocity of 15.0 m/s overtakes and passes the car. (a) Calculate the time necessary for the car to reach the truck. (b) Calculate the distance beyond the traffic light that the car will pass the truck. (c) Determine the speed of the car when it passes the truck.

Answer 1

Step-by-step explanation:

(a) The time necessary for the car to reach the truck can be calculated using the equation for average velocity:

v_avg = v0 + at

where v0 is the initial velocity of the car (which is 0 m/s at the instant the light turns green), a is the acceleration of the car (2.00 m/s^2), and t is the time elapsed.

Since the truck is traveling with a constant velocity of 15.0 m/s, we can equate the average velocity of the car to the velocity of the truck:

v0 + at = 15.0 m/s

Solving for t, we get:

t = (15.0 m/s - v0) / a = 15.0 m/s / 2.00 m/s^2 = 7.50 s

(b) The distance beyond the traffic light that the car will pass the truck can be calculated using the equation for displacement:

d = v0t + 1/2at^2

Plugging in the values we found above, we get:

d = (0 m/s)(7.50 s) + 1/2(2.00 m/s^2)(7.50 s)^2 = 56.25 m

(c) The speed of the car when it passes the truck can be calculated using the equation for velocity:

v = v0 + at = 0 m/s + (2.00 m/s^2)(7.50 s) = 15.0 m/s