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

Figure from experiment 9 from Real-World Math with Vernier

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.

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 »

Activity 9 from Real-World Math with Vernier Lab Book

<i>Real-World Math with Vernier</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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