### Introduction

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.

### Objectives

• 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.