Physics question

Question

A car is stopped at a red light. Meanwhile, a truck is approaching the stoplight at a constant velocity of 15 m/s, making it just when the light turns green. When the light turns green, the car accelerates at 4 m/s^2. How far will it have to travel until it reaches the truck? 

I don’t understand what I’m solving for here. It doesn’t look like a proportional reasoning question, but there are two vehicles present with different velocities, acceleration etc. Do I neglect the information on the truck and just set up variables for the car, solving for delta x using a kinematic equation?

Answer 1

Hi Deinonychus. I understand why you are confused. The question, as written, did not include certain details which I will now attempt to fill in for you. The car is not moving as it waits for the traffic light to turn green. While this is occurring, a truck, behind the car and some distance away from the car, is moving towards the traffic light and as it gets to the traffic light, the traffic light turns green. Hence, the truck does not stop and continues moving through the traffic light and passes the stationary car. In the meantime, the car starts moving to catch up the truck. The question asks what distance must the car move from its starting point to catch the truck. In order to solve this distance, you have to first find out what time is needed by the car to catch the truck. Once you have determined that time you can then use it to determine the distance the car must travel to catch the truck. Hope this explanation helps you get a better visual of what is happening.

Answer 2

Well suppose the car passes the truck t seconds after the light turns green.

The truck will have travelled 15t m from the stop light.

s = ut + 0.5at²

For the car u=0, a= 4, so the car will have travelled 0.5 x 4 x t² m = 2t²

When the car meets the truck 2t² = 15t, so t = 15/2

And distance travelled from stoplight = 15t = 225/2 m.