The cart is initially at rest. The overall goal will be to determine the cart’s acceleration. Plot the data in such a way that:
The position is the independent variable, and plotted on the horizontal axis.
The acceleration is inversely proportional to the slope.
The resulting plot is a straight line.. (Start with x = ½ a t^2 and use algebra )
There will be a table of the distance and time of the car.
x = ½ a t^2
The Attempt at a Solution
My biggest confusion with this is what will be on the vertical axis. If the acceleration is inversely proportional to the slope, then wouldn't the units of acceleration just be flipped in order to match the slope? Basically, wouldn't the vertical axis be time squared? That doesn't make any sense to me, as time is generally not on the vertical axis, but it also cannot be in the horizontal axis as the criteria asks that the position is the horizontal axis.
I think in order to meet the 3rd point, I must make the original equation into a natural log plot, where:
ln(x) = ln(½) + ln(a) + ln(t^2). Would that be the correct way to go about this?
Any and all help is deeply appreciated!