Constant Acceleration Ratio to Constant Velocity

[Bill48]

Homework Statement

A car traveling at an unspecified constant speed passes a parked motorcycle cop. The motorcycle accelerated at an unspecified constant acceleration and reaches the car at unspecified distance d. At what point did the motorcycle's speed match that of the car, expressed as a ratio of d divided by a denominator.

Homework Equations

None that I know of.

The Attempt at a Solution

This question was on a test. Per the professor no one in the class got it. The answer is d/4. I've been trying to figure out how that was obtained but have no idea. It is obviously a universal ratio since the value of velocity and acceleration are not given.

 

[Borg]

The car and the motorcycle both use the same equation. Do you know the equation?

 

[Bill48]

X = Xi + Vi(t) + 1/2 a t^2 is the closest equation I can think of. Xi is initial location, Vi is initial velocity. a is acceleration. But since I have no values I don't know how to proceed.

 

[Borg]

You do have initial values.

1. What is X₀ for each person?
2. What is v₀ for each person?
3. What is a for each person?

 

[Bill48]

X0 is the same for both. V0 for the car is not given, but is zero for the motorcycle. A for the car is zero since it is traveling at a constant velocity. A for the motorcycle is constant but not given.

 

[Borg]

Correct. Now what is the relationship of their distance traveled and how can you write that in a single equation?

 

[Bill48]

The relationship of their distance traveled is d/4. The prof gave us the answer when he returned our papers. I have no idea how that answer was obtained.

 

[Borg]

What is the final distance equation for the car with the zero elements removed?

 

[Bill48]

I have no idea, that's why I posted the question. If you're not going to explain then quit wasting my time.

 

[Borg]

I am not wasting your time. I am trying to help you understand how to solve it. The rules for homework questions are that people cannot just give answers.
You gave me the equation of motion for the car and motorcycle so it should be a simple thing to write them without the zero terms.

 

[Bill48]

I know the answer. The answer is d/4.

 

[Biker]

I know the answer. The answer is d/4.

Getting the solution directly won't get you anywhere.

Once you get the equations without zero terms. What does the df represent in each equation? Can you use it in away to perhaps combine the equations together?

You will get to a really interesting fact. Use the kinematic equations again to get the value of time need to for the motorcycle's velocity to equal the cars velocity.

The rest is obvious.

 

[PeroK]

Homework Statement

A car traveling at an unspecified constant speed passes a parked motorcycle cop. The motorcycle accelerated at an unspecified constant acceleration and reaches the car at unspecified distance d. At what point did the motorcycle's speed match that of the car, expressed as a ratio of d divided by a denominator.

Homework Equations

None that I know of.

The Attempt at a Solution

This question was on a test. Per the professor no one in the class got it. The answer is d/4. I've been trying to figure out how that was obtained but have no idea. It is obviously a universal ratio since the value of velocity and acceleration are not given.

You could have thought like this:

If this problem can be solved it must be the same solution for all velocities and accelerations. So, perhaps just choose any numbers and try to solve the problem. Then, perhaps, choose a different set of numbers and try to solve the problem again.

E.g. speed = $20 m/s$, acceleration = $5m/s^2$. You can now calculate the two distances and compare them.

Then, try again with a different velocity and acceleration.

You should find that in both cases the total distance is 4 times the first distance.

Solving with specific numbers might give you some ideas on how to solve the general problem, which is going to be all algebra and no arithmetic.