Kinematic Equations: Find the time t when two objects meet

[StephanieSamperio]

Homework Statement

Object A is at X=0m. Beginning at a time 0 s, A accelerates from rest at 2 m/s^2 in the positive x-direction. Object B is at X = 50 m at t = 0s and begins moving towards A from rest with an acceleration of magnitude 4m/s^2.

Part A) Where do A and B meet?
Part B) How fast is A moving when they meet?

Relevant Equations

Xf = xi + vi(t)+1/2(a)(t^2)
Vf = Vi+a(t)

Part A)
So, I set the two positions equations of A and B equal to each other since the position has to be the same.

A: 0 + 0 + 1/2(2)t^2 = 50 + 0 + 1/2(4)t^2 :B

I know I have to solve for time t, but there's no way to solve it with both sides having t^2 so I am not sure which variables I got wrong for the objects.

 

[BvU]

Hello Stephanie, !

If you draw a picture, you will quickly see that B does not move towards A in your expression. Can you explain why not ?

 

[PhanthomJay]

Your equation reads

T^2 = 50 + 2T^2. That equation is easily solved for T. But your equation has a signage error.

 

[StephanieSamperio]

Hello Stephanie, !

If you draw a picture, you will quickly see that B does not move towards A in your expression. Can you explain why not ?

Hi!

I think I could explain. B is already ahead by 50 m meaning it would have to be in constant acceleration while A catches up

 

[StephanieSamperio]

Your equation reads

T^2 = 50 + 2T^2. That equation is easily solved for T. But your equation has a signage error.

If there's two t^2 wouldn't they cancel out instead of being solved for?

 

[BvU]

Hi!

I think I could explain. B is already ahead by 50 m meaning it would have to be in constant acceleration while A catches up

No, then B still would move in the same direction as A and the given is that it does not. So there is something wrong with your expression. Draw a picture.

If there's two t^2 wouldn't they cancel out instead of being solved for?

You would get that if accelerations of A and B would have the same value: A and B are 50 m apart and they stay 50 m apart. Again, because in your expression B does not move towards A

 

[StephanieSamperio]

This is the picture I drew. Would object A need to have a velocity to be able to meet with Object B? I believe my mistake in my equations is with Object A

 

[BvU]

How come the arrow at B points in a different direction than the one at A ?
(whilst they appear in the same way in your expression ...)

 

[StephanieSamperio]

How come the arrow at B points in a different direction than the one at A ?
(whilst they appear in the same way in your expression ...)

In the question, it says Object B is moving towards A from rest which is why I drew them in different directions

 

[PhanthomJay]

In the question, it says Object B is moving towards A from rest which is why I drew them in different directions

But the equation you wrote has them moving in the same direction.

 

[BvU]

So, @StephanieSamperio : how do you get B to move towards A (i.e. towards x = 0 , i.e. make x_B decrease instead of increase) in your equations ?