Graphing Distance and Time to find Acceleration

[Terrence]

Homework Statement

I have to do an experiment tomorrow, in which we roll a cart down an inclined plane to find the acceleration of the cart. We are given set distances (20, 40, 60, and 80 cm) and will be told to time how long it takes the cart to go said distances. Once we have this information, we must create a graph to find the acceleration of the cart.

The catch is, we have to take the Natural Log (ln) of one, or both, parts of the data to create a straight line in our graph, and use the slope of that line to find the acceleration.

Homework Equations

D = .5*a*t^2

The Attempt at a Solution

I cannot figure out which side of the equation to take the ln of. I believe its the distance side, making ln(d) = .5*a*t^2, but I'm not sure.

Since I have not yet done the experiment I don't have any times to give (sorry ) but I'm pretty sure that isn't required for what I'm asking.

 

[Apphysicist]

I have no idea why you would take ln of anything with this.

You're graphing d=mt^2...m=0.5a.

So you would want to graph d v. t^2 (d is y-axis, t^2 is x-axis) to give a straight line and take its slope.

 

[cepheid]

I cannot figure out which side of the equation to take the ln of.

Anything that you do to one side of the equation, you must also do to the other side. This is always the case. Otherwise the two sides will no longer be equal.

So, you have to take the natural log of both sides of the equation.

 

[Terrence]

Apphysicist - Yeah that makes sense... I thought about it, but for some reason couldn't get ln out of my head. We've used it the most throughout this course. Thanks a lot.

cepheid - Thats what I was thinking too, which is why I was having so much trouble with this lol. I dunno, guess I just wasn't thinking straight. Thanks a lot guys.

 

[rwisz]

I would recommend taking the natural log of both sides of the equation D = .5*a*t^2. This will result in ln(D) = ln(.5*a*t^2). By taking the natural log of both sides, you will be able to create a linear relationship between ln(D) and ln(t^2), which will make it easier to calculate the slope and determine the acceleration. Additionally, taking the natural log of both sides allows you to use the properties of logarithms to simplify the equation and solve for the acceleration. I would also suggest including error bars on your graph to account for any uncertainties in your measurements. Good luck with your experiment!