# Relationship Between the Distance and Time of a Falling Object

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#### Updated on Jan 29, 2014

Freefall occurs where the only force acting on an object is gravity. Because gravitational acceleration on earth is constant, the distance an object falls is proportional to the time spent falling. In this experiment, you will experimentally determine the acceleration due to gravity in addition to testing your own reaction time! Reaction time is the time it takes for you to react to an event: in this case, the falling of a meter stick or dollar bill. Is your reaction time faster than acceleration due to gravity?

### Objective

Experimentally determine acceleration due to gravity.

Do all objects fall at the same rate? Does the weight of the object matter? What is the relationship between distance and time for free-falling objects?

### Materials

• Friend, partner or helper
• Small ball
• Meter stick
• Dollar bill
• Stopwatch
• Notebook and pencil

### Procedure

1. Have a partner hold the meter stick so the 0 side is just above your hand.
2. Have the partner start the timer as soon as he or she drops the meter stick and stop the timer as soon as you catch it.
3. Record the distance along the meter stick and the time.
4. Do this several times for different lengths along the meter stick. What is the relationship between the time and the distance the meter stick traveled?
5. Graph your results. Time will be on the x-axis, distance traveled in meters will be on the y-axis.
6. Use the following equation to calculate the time it takes for the meter stick to fall. How close is your calculated time to your stopwatch value?

• Where d is the distance the object traveled, in meters
• g is the gravitational acceleration on Earth, equal to 9.81m/s2
• t is the time in seconds.
1. Calculate the acceleration at any point on the graph. How close is it to the gravitational acceleration of Earth?

1. Repeat the experiment with a dollar bill. Use the above equation to calculate how long it will take for the length of the dollar to pass through your fingers. Can you catch it?

### Results

Graphing results will show that distance traveled is in proportional to the square of the time spent falling. Your calculated acceleration should be close to 9.81 m/s2. Human reaction time is approximately 0.25 seconds which, for the majority of people, is not fast enough to catch a dollar bill.

### Why?

The graph you create will show that the longer the meter stick falls, the faster it ends up moving. This explains the curve in the graph: because of the constant acceleration produced by the force of gravity, the velocity of an object will get increasingly faster.

When objects are in true free fall, they will eventually reach their terminal velocity when the downward force from gravity and the upward force from air resistance are equal. A good anaology would be a skydiver: even though gravity still acts on her body, she wouldn’t get any faster because the force of the air pushing back is so great. In this experiment, air resistance and drag are not really an issue because the objects fall very short distances.