Question

At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.60m/s2 . At the same instant, a truck, traveling with a constant speed of 14.9m/s , overtakes and passes the automobile.

How far beyond its starting point does the automobile overtake the truck? (in meters)

Answer 1

The car overtakes the truck by traveling approximately 11.95 meters beyond its starting point.

Step-by-step explanation:

To answer this question, we need to find the time it takes for the truck and the car to be closest to each other and the distance between them at that point. We can do this by finding the time it takes for the car to travel 32 km at its constant velocity, and then subtracting the time it takes for the truck to travel the same distance at its constant velocity. Let's start by finding the time it takes for the car:

1. Convert the car's velocity from km/h to m/s: 50 km/h = 50 * (1000/3600) m/s = 13.9 m/s
2. Use the formula time = distance / velocity to find the time it takes for the car to travel 32 km: t = 32 km / 13.9 m/s = 2.30 s

Next, let's find the time it takes for the truck:

1. Convert the truck's velocity from km/h to m/s: 80 km/h = 80 * (1000/3600) m/s = 22.2 m/s
2. Use the formula time = distance / velocity to find the time it takes for the truck to travel 32 km: t = 32 km / 22.2 m/s = 1.44 s

Finally, we can find the time when the car and the truck are closest to each other by subtracting the time it takes for the truck from the time it takes for the car: t = 2.30 s - 1.44 s = 0.86 s

Now, let's find the distance between the car and the truck at that point:

1. Use the formula distance = velocity * time to find the distance the car travels in 0.86 s: d = 13.9 m/s * 0.86 s = 11.95 m

So, the car overtakes the truck by traveling a distance of approximately 11.95 meters beyond its starting point.