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

• StephanieSamperio
In summary: But the equation you wrote has them moving in the same direction. 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 ?
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.

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 ?

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

BvU said:
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

PhanthomJay said:

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?

StephanieSamperio said:
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.

StephanieSamperio said:
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

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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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 ...)

BvU said:
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

StephanieSamperio said:
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.

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 ?

## 1. What are the kinematic equations?

The kinematic equations are a set of four equations used to solve for the motion of an object in terms of its displacement, velocity, acceleration, and time. They are commonly used in physics and engineering to analyze the motion of objects.

## 2. How do I use the kinematic equations to find the time when two objects meet?

To find the time when two objects meet, you first need to determine the initial positions, velocities, and accelerations of both objects. Then, you can use the kinematic equations to set up a system of equations and solve for the time when both objects have the same position.

## 3. What information do I need to know to use the kinematic equations?

To use the kinematic equations, you need to know the initial position, velocity, and acceleration of the objects in question. Additionally, you need to know the distance or displacement between the two objects and the direction of their motion.

## 4. Can the kinematic equations be used for any type of motion?

Yes, the kinematic equations can be used for any type of motion as long as the acceleration remains constant. This includes linear, circular, and projectile motion.

## 5. Are there any limitations to using the kinematic equations?

One limitation of the kinematic equations is that they only apply to objects with constant acceleration. Additionally, they do not take into account external forces such as air resistance or friction, which can affect the motion of an object.

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