What to plot against t^1/5 to get a straight line from kinematics data?

[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?
$$d = \frac{1}{2}at^2$$
$$d^\frac{1}{10} = (\frac{1}{2}a)^\frac{1}{10} t^\frac{1}{5}$$

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

 

[quantumdude]

Sorry for the late reply.

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

* Get $t^{1/5}$ 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 $y=mx$ after you solve for $t^{1/5}$.