Distance, acceleration, and time

[HopeDagger]

Hey there, everyone. Looks like some splendid forums you've got here. This isn't really a homework question, but rather an application I am developing. However, the (lack of) complexity of the question seems to warrant it the best location here. :)

Alright, here's the issue in its generic form:

I have D, the distance that must be traveled.
I have A, the acceleration constant of the camera.

And I need to find T, the time it takes to cover the distance if the speed is accelerating at A/sec.

Then there's the tougher part. To make camera movement smooth, I need the camera to reverse its acceleration halfway to the target, and slow down to a smooth stop at the end of the distance to be covered. This might not really fit into the physics, and be more of a programming issue for me to handle. If so, no problem, I'm more so concerned with the core problem at the top.

I'm certainly being picky, but any help is most graciously appreciated! Thanks! :)

 

[zwtipp05]

Hey there, everyone. Looks like some splendid forums you've got here. This isn't really a homework question, but rather an application I am developing. However, the (lack of) complexity of the question seems to warrant it the best location here. :)

Alright, here's the issue in its generic form:

I have D, the distance that must be traveled.
I have A, the acceleration constant of the camera.

And I need to find T, the time it takes to cover the distance if the speed is accelerating at A/sec.

Then there's the tougher part. To make camera movement smooth, I need the camera to reverse its acceleration halfway to the target, and slow down to a smooth stop at the end of the distance to be covered. This might not really fit into the physics, and be more of a programming issue for me to handle. If so, no problem, I'm more so concerned with the core problem at the top.

I'm certainly being picky, but any help is most graciously appreciated! Thanks! :)

Use the equation: D = .5*a*T^2

 

[James R]

So, what you seem to be saying is you want the camera to accelerate smoothly at rate A for distance D/2, then decelerate smoothly (also at rate A?) until it reaches distance D.

The time required for the acceleration, if the camera starts from rest, will be given by

$$D/2 = \frac{1}{2} At^2$$

which gives

$$t = \sqrt{\frac{D}{A}}$$

Since the problem is symmetrical, the total time to move the entire distance D will be twice this value.

 

[HopeDagger]

You guys are fantastic (and quick!). Thanks a bunch.