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What Goes Up – Position and Time for a Cart on a Ramp

Experiment #9 from Real-World Math with Vernier

Education Level
High School


When a cart is given a brief push up a ramp, it will roll back down again after reaching its highest point. Algebraically, the relationship between the position and elapsed time for the cart is quadratic in the general form

y = a{x^2} + bx + c

where y represents the position of the cart on the ramp and x represents the elapsed time. The quantities a, b, and c are parameters which depend on such things as the inclination angle of the ramp and the cart’s initial speed. Although the cart moves back and forth in a straight-line path, a plot of its position along the ramp graphed as a function of time is parabolic.


  • Record position versus time data for a cart rolling up and down a ramp.
  • Determine an appropriate parabolic model for the position data using the x– and y– intercept information.

Sensors and Equipment

This experiment features the following sensors and equipment. Additional equipment may be required.

Option 2


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This experiment is #9 of Real-World Math with Vernier. The experiment in the book includes student instructions as well as instructor information for set up, helpful hints, and sample graphs and data.

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