Physics help - finding what slope means

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To create a straight line graph from position-time data with an initial velocity of zero, the student should plot time raised to the power of one-fifth (t^1/5) on the y-axis and position (d) on the x-axis. The relationship between the slope of the line and the acceleration of the cart can be derived from the equation d = (1/2)at^2, leading to the conclusion that the slope represents (1/2)a^(1/10). By rearranging the equation to fit the linear form y = mx, the student can identify the slope as a function of acceleration. This approach allows for a clear understanding of how acceleration affects the cart's motion. Understanding these relationships is crucial for mastering the concepts of kinematics in physics.
an_mui
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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?
 
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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}.
 

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