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?
Homework 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 im not sure which variables I got wrong for the objects.

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BvU

Homework Helper
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

Homework Helper
Gold Member

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

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

Homework Helper
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

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BvU

Homework Helper
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

Homework Helper
Gold Member
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

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

"Kinematic Equations: Find the time t when two objects meet"

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