Calculating An Acceleration To Arrive With Zero Velocity

[eddieparker]

Hello!

I'm new to the forums, so apologies if I've put this in the wrong forum. I was debating on placing this in the 'Homework' section, but this is really just a problem I'm having with an application I'm writing, so I wasn't sure if it applied. Anyhow, please file accordingly, and I'll know better for next time.

Anyhow, it's been years since I've used my physics, and I'm quite rusty. I'm working on an application which is trying to return an acceleration for an object that is moving in a frictionless world. At any point in time, I have access to its:

- Velocity
- Position
- Goal

What I'd like to do is have the function return the appropriate deceleration such that it arrives at it's goal with zero velocity.

I'd appreciate anything from pointers to formula's, to discussions regarding possible solutions, etc.

The key thing is that I don't have access to anything save the time since the last calculation, and I'd prefer not to specify the amount of time for the deceleration to occur (that is, I'd prefer the deceleration to scale depending on the velocity).

Your help, advice, and pointers are appreciated.

Cheers!

-e-

 

[berkeman]

Hello!

I'm new to the forums, so apologies if I've put this in the wrong forum. I was debating on placing this in the 'Homework' section, but this is really just a problem I'm having with an application I'm writing, so I wasn't sure if it applied. Anyhow, please file accordingly, and I'll know better for next time.

Anyhow, it's been years since I've used my physics, and I'm quite rusty. I'm working on an application which is trying to return an acceleration for an object that is moving in a frictionless world. At any point in time, I have access to its:

- Velocity
- Position
- Goal

What I'd like to do is have the function return the appropriate deceleration such that it arrives at it's goal with zero velocity.

I'd appreciate anything from pointers to formula's, to discussions regarding possible solutions, etc.

The key thing is that I don't have access to anything save the time since the last calculation, and I'd prefer not to specify the amount of time for the deceleration to occur (that is, I'd prefer the deceleration to scale depending on the velocity).

Your help, advice, and pointers are appreciated.

Cheers!

-e-

Welcome to the PF. I went ahead and moved the thread -- this is the best place for it.

You will use the kinematic equations of motion, for a constant acceleration (that is the simplest form, and should work for what you want to do).

http://en.wikipedia.org/wiki/Kinematics (scroll down to the Kinematics of Constant Acceleration)

They are equations that relate position, velocity and acceleration. See if that helps, and ask specific questions if you are confused about something. Have fun on the project!

 

[kerimek]

Hello!

Calculating the appropriate acceleration for an object to arrive at a specific position with zero velocity can be achieved using the following formula:

a = -v^2 / (2 * (x - x0))

Where:
a = acceleration
v = initial velocity
x = goal position
x0 = initial position

This formula is derived from the equation of motion for constant acceleration, d = v0t + 1/2at^2, where d is the displacement, v0 is the initial velocity, a is the acceleration, and t is the time.

In this case, we can rearrange the equation to solve for acceleration, given that the final displacement (x) is equal to the initial displacement (x0) and the final velocity is zero.

I hope this helps with your application. Let me know if you have any further questions or need clarification.