# What Goes Up - Position and Time for a Cart on a Ramp

Recommended for High School.

## 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

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 cartâ€™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.

## Sensors and Equipment

This activity features the following Vernier sensors and equipment.

### Option 1

### Option 2

### Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

## Standards Correlations

See all standards correlations for *Real-World Math with Vernier* »

*Real-World Math with Vernier*

*Real-World Math with Vernier*

See other experiments from the lab book.