Another motion problem for constant acceleration

[chroncile]

Homework Statement

A truck travels at a constant speed of 28.0 m/s in the fast lane of a two-lane highway. It approaches a stationary car stopped a the side of the road. When the truck is still 125 m behind the car, the car pulls out into the slow lane with an acceleration of 2.6 m/s². How long will it take the truck to reach the car? (Answer is 6.32 s)

Homework Equations

N / A

The Attempt at a Solution

I have no idea how to do this :(

 

[Doc Al]

This is similar to the wolf/rabbit problem.

Write the position as a function of time for both the truck and the car. Measure from the initial position of the truck when the car starts moving. Set them equal.

 

[chroncile]

I'm sorry, but could you please write that out in equation form? I am not a clever man.

 

[Doc Al]

Oh, you're clever enough.

You just solved an almost identical problem! Hint: The truck moves at constant speed; the car accelerates.

 

[rwisz]

I would approach this problem by first identifying the known values and variables. The known values in this problem are the truck's constant speed of 28.0 m/s, the distance between the truck and the car (125 m), and the car's acceleration of 2.6 m/s2. The variable we are trying to solve for is time (t).

Next, I would use the kinematic equation for constant acceleration, which is d = vit + 1/2at^2, where d is the distance, vi is the initial velocity, a is the acceleration, and t is the time. We can rearrange this equation to solve for t, which gives us t = (-vi ± √(vi^2 + 2ad)) / a.

Plugging in the known values, we get t = (-28.0 ± √(28.0^2 + 2(2.6)(125))) / 2.6. This gives us two possible values for t, but we can disregard the negative value since time cannot be negative. Therefore, the truck will take 6.32 seconds to reach the car.

In conclusion, by using the kinematic equation for constant acceleration, we can determine the time it will take for the truck to reach the car after the car pulls out into the slow lane. This type of problem is commonly used in physics to calculate the motion of objects with constant acceleration.