At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.70 m/s^2. At the same instant, a truck, traveling with a constant speed of 15.4 m/s , overtakes and passes the automobile. Required:
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.

a)  t = 11.407 s, b)   x = 175.66 m,  v = c)         v = 30.80 m / s

Explanation:

a) This is a kinematics exercise, let's write the equation of each vehicle

car

          x = x₀ + v₀ t + ½ a t²

Let's fix our reference system at the point where the car is, indicate that the car stops from rest vo = 0

          x₀ = v₀ = 0

we substitute

          x = ½ a t²

truck

         x₂= v₀ t

         v₀ = 15.4 m / s

at the point where they are, their positions are equal

       ½ a t² = vo t

        t = 2 vo / a

calculate us

        t = 2 15.4 / 2.70

        t = 11.407 s

b) the distance to reach it

        x = ½ to t²

        x = ½ 2.70 11.407²

        x = 175.66 m

c)  the speed of the car is

       v = vo + a t

       vo = 0

       v = at

       v = 2.70 11.407

       v = 30.80 m / s