Comparison of velocity at the end of distance

[gijungkim]

Homework Statement

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities vA and vB of the bodies at the end of distance D are related by

a.vB = vA.

b.vB = vA.

c.vB = 2 vA.

d.vB = 4 vA.

e.vA = 2vB.

Homework Equations

F = ma
x = vot + 0.5 at^2
Vf = Vo + at

The Attempt at a Solution

Answer is B but I have no clue why
First, I just picked a random number to make it easier. I picked acceleration of 2m/s^2 for A and 4m/s^2 for B (since it has twice more force than A)
and I picked x as 1m
Then I'll get
1 = 0 + 0.5 * 2 * t^2, t = 1 for A
1 = 0 + 0.5 * 4 * t^2, t = 0.707 for B
If I plug this into Vf = V0 + at
Vf = 2 for A
Vf = 2.83 for B...
To me vB = vA doesn't make sense.. Can anyone help me

 

[TSny]

Was there any information given regarding the directions of the forces?

 

[PeroK]

Answers a. and b. are the same. Are you sure b. isn't something else?

Your calculations are correct. Can you see a way to generalise them to get the answer?

 

[gijungkim]

Was there any information given regarding the directions of the forces?

That is exactly what question stated. I copied and pasted it.

 

[gijungkim]

Answers a. and b. are the same. Are you sure b. isn't something else?

Your calculations are correct. Can you see a way to generalise them to get the answer?

Probably the answer is wrong haha I'm just using random questions from the internet to practice so.

 

[PeroK]

Probably the answer is wrong haha I'm just using random questions from the internet to practice so.

It would be good practice to get the answer for this without multiple choice.

You could generalise the calculations you've already done. Or you could consider energy.

 

[gijungkim]

It would be good practice to get the answer for this without multiple choice.

You could generalise the calculations you've already done. Or you could consider energy.

Is the answer V2 = sqrt 2 * V1 ?

 

[PeroK]

Is the answer V2 = sqrt 2 * V1 ?

It is!

 

[gijungkim]

It is!

Thank you! :)