Help with calculating the range of error accleration

[Digitalx04]

Homework Statement

Motion on an Incline. I did an experiment where I measured the acceleration of a cart rolling down an inclined plane using 5 different angles and comparing them to those predicted in Newton's 2nd law of motion.

I am trying to figure out the equation I can use to find the $$\Delta$$a using the average deviation in the time as $$\Delta$$t. I am treating d (the displacement of the car I used in the experiment) as an exact measurement.

Homework Equations

I used d = $$\frac{1}{2}$$at^2 in a previous experiment and solving for a again would yield me a = $$\frac{2d}{t^2}$$. I figured I could use this same derivation to solve for $$\Delta$$a which may or may not be my problem.

I also know by Newton's 2nd law that $$\vec{F}$$= m$$\bar{a}$$ and that that a = g sin$$\theta$$

The Attempt at a Solution

I tried the range of error for a = $$\frac{2d}{t^2}$$ coming out with :
$$\Delta$$a = 2$$\Delta$$d/$$\Delta$$t^2 but this dosn't seem right. Any suggestions would be greatly appreciated. Thanks.

 

[Digitalx04]

After some more fiddling I came up with a new equation for $$\Delta$$a being:

$$\Delta$$a = a($$\frac{\Delta d}{d}$$ + $$\frac{2\Delta t}{t}$$)

Would this be the correct formula?

 

[Redbelly98]

Yes, that's right.

p.s. welcome to Physics Forums.

 

[Digitalx04]

Thanks a lot,one more question. When I am doing these graphs it asks me to plot acceleration as a function of mass and another graph of my experimental acceleration as a function of sin. This means that my x-axis for both of these should be my acceleration and my y-axis the dependent variable of sin or mass in each different graph correct?

 

[Redbelly98]

By convention, we usually graph y as a function of x. So a would be along the y-axis in both cases.