# Accelerated Motion

## Materials:

- lab sheet and writing utensil
- calculator
- spreadsheet software graphing capability
- 8.5″ x 11″ card stock
- ruler with
**mm**markings

## Goals

The goals of the lab are to:

- apply a kinematic equation to predict the accelerated motion of an object in free-fall
- acquire data on human reaction time
- analyse the data in a scientific way to determine and report your average reaction time with uncertainty.

## Experimental Setup

Cut the card stock into three 11″ long strips.

Draw a horizontal line halfway across one strip, about 4 **cm **above the bottom edge. Label the line “start here”

Use a kinematic equation to calculate the distance an object in free-fall would drop in 0.02 seconds. Show your work below.

Convert your answer to **cm**, show your work below.

Starting from your “start here” line, measure upward a distance equal to your answer above and draw another line half way across the strip. Label this line “0.02 **s”**

Repeat this calculation at 0.02 **s **intervals and continue measuring and marking the drop distances up from the “start here” line until you go beyond the top of the strip. Label each line with the fall time used to calculate the distance to that line. Either use the formula feature of the spreadsheet software or use your calculator and enter each answer by hand into the spreadsheet. You should get a table like this, but with many more rows:

Time (s) |
Drop Distance (cm) |

0.02 | XX |

0.04 | XX |

….. | ….. |

Are the lines on your card strip evenly spaced? If not, why not?

If you were to graph the data in your spreadsheet, what would the graph look like, and why?

Graph the data in your spreadsheet and fit a quadratic function to the data. According to the R^{2} value, does the quadratic function fit the data well? Explain.

## Experimental Methods

Have a friend or family member hold the card at the top. You place your thumb and index finger about 3 **cm** apart on either side of the “start here” line, as if you were going to pinch the card.

At a random time, the holder will drop the card and you will close your fingers to catch the card. Use the markings to read off the time you took to see the card falling and close your fingers. This is your reaction time. Repeat this experiment 10 times, recording the measured reaction time for each trial. You will not always land exactly on a line, so there will be uncertainty in your measurements. Record the uncertainty in your estimate of the measured time for each trial. Fill in the table below:

Trial | Time (s) | Uncertainty (s) |

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | ||

7 | ||

8 | ||

9 | ||

10 |

## Data Analysis

Calculate the average and standard deviation of your 10 measurements. You may use the feature of the spreadsheet to make these calculations for you.

Using the standard deviation as an estimate of your uncertainty in the average reaction time, report your reaction time with uncertainty in the standard format:

## Conclusions

We made a major assumption in using the kinematic equations to calculate the distance the card would fall in a certain time. We assumed the card had a constant acceleration of a known value, specifically 9.8 **m/s/s**. In other words our *model* assumed the card was in free-fall and ignored the drag force on the card. Explain whether or not applying a free-fall model was appropriate in this situation, based on your knowledge of how the drag force works.

Find a peer-reviewed research article on human reaction time and compare the result of that study to your result. Does your result seem reasonable in comparison? Do the values agree within the combined uncertainty in your measurement and theirs?

Their experiment was likely not exactly the same as yours. Contrast their experiment with yours and explain how differences in experimental setup and methods might lead to differences in your values and in your uncertainties.

Are there any sources of systematic error that you did not account for in your experiment? If so, using exactly the same materials, what would you do differently to eliminate that systematic error from your experiment?

If you were to perform the experiment again, with exactly the same materials, what would you do differently to improve the precision of your experimental methods?

Do you feel that the uncertainty in your average reaction time was caused by a lack of precision in your experimental methods or by an underlying real variation in your actual reaction time for each trial? Explain.