physics help - finding what slope means

an_mui

Suppose a student is given position-time data for a cart which was known to have an initial velocity of zero. if the student plots the fifth root of time (t^1/5) on the y axis, what variable should he plot on the x axis so that the resulting graph is a straight line? how is the slope of the line related to the acceleration of the cart?
[tex]d = \frac{1}{2}at^2[/tex]
[tex]d^\frac{1}{10} = (\frac{1}{2}a)^\frac{1}{10} t^\frac{1}{5}[/tex]

this is what i've done so far.... can anyone give me some hints as to what to do next?

Tom Mattson

Sorry for the late reply.

* Get [itex]t^{1/5}[/itex] by itself.
* Identify the independent variable (the one that is plotted on the x-axis).
* Identify the slope.

This can be done by comparing your equation to the equation [itex]y=mx[/itex] after you solve for [itex]t^{1/5}[/itex].