Question

A truck is stopped at a stoplight. When the light turns green, the truck accelerates at 2.5 m/s². At the same instant, a car passes the truck going 19 m/s. Where and when does the truck catch up with the car?

Answer 1

The truck catches up with the car after approximately 15.2 seconds and at a distance of 289 meters.

Step-by-step explanation:

To determine where and when the truck catches up with the car, we need to analyze their motion. The truck starts from rest and accelerates at 2.5 m/s², while the car is already moving at a constant velocity of 19 m/s. We can use the equations of motion to find the time it takes for the truck to catch up with the car.

Let's assume that the truck catches up with the car after a time t. During this time, the car will have traveled a distance of dcar = 19t. The truck starts from rest, so the distance it travels can be calculated using the equation dtruck = (1/2)at², where a is the acceleration and t is the time. Equating the distances and solving for t, we get:

19t = (1/2)(2.5)t²

19 = 1.25t

t ≈ 15.2 seconds

Using the time t, we can find the distance at which the truck catches up with the car:

dcar = 19t ≈ 289 meters

Therefore, the truck catches up with the car after approximately 15.2 seconds and at a distance of 289 meters.