Question

a car that has stopped at a toll booth leaves the booth witha constant acceleration of 4 ft/s2. at the time the car leavesthe booth it is 2500 ft behind a truck traveling with a con-stant velocity of 50 ft/s. how long will it take for the carto catch the truck, and how far will the car be from the tollbooth at that time?

Answer 1

The car will take 12.5 seconds to catch the truck, and it will be approximately 313.25 ft from the toll booth at that time.

Step-by-step explanation:

To determine how long it will take for the car to catch the truck:

First, we need to find the initial distance between the car and the truck. The car is 2500 ft behind the truck.

Next, we need to calculate the time it takes for the car to catch up to the truck.

We can use the formula: time = (final velocity - initial velocity) / acceleration. The car has a constant acceleration of 4 ft/s² and the truck has a constant velocity of 50 ft/s.

The final velocity of the car can be found using the formula: final velocity = initial velocity + acceleration * time.

Substituting the values into the formulas, we have:

time = (50 ft/s - 0 ft/s) / 4 ft/s²

= 12.5 seconds.

Therefore, it will take 12.5 seconds for the car to catch the truck. Now, let's find out how far the car will be from the toll booth at that time:

We can use the formula: distance = initial velocity * time + 0.5 * acceleration * time².

Substituting the values, we have:

distance = 0 ft/s * 12.5 seconds + 0.5 * 4 ft/s² * (12.5 seconds)²

= 313.25 ft.

So, at the time the car catches the truck, it will be approximately 313.25 ft from the toll booth.