# Kinematics

## Procedure

We will use the formula yf = yo + voy t + ½ ay t2, valid for constant acceleration, in the following two experiments:

### Part 1

Use freely falling rulers to measure your reaction time.
• Take g = 9.80 m/s2 ± 0.01 m/s2.
• The lab partner whose reaction time is being measured will place his/her forearm on the lab bench with the fingers overhanging the edge. This is to prevent the testee from moving their arm downwards, chasing after the falling ruler.
• The other lab partner will suspend the ruler between the the first partner's thumb and finger, held about 1 cm apart. The second partner will drop the ruler without warning while the first partner attempts to catch it.
• Practice a few times, but do not record these data.
• Record the distance at which the ruler was caught.
• For the error in the distance, use your finger width.
• Repeat several times (you decide how many).
• Do not mix your data with those of your partner; each student should calculate his/her individual reaction time.
• Most human reaction times will fall between 0.1 and 0.2 seconds.

### Part 2

Determine the acceleration of a cart down an inclined slope.
• Place a block under one end of the ramp to elevate it slightly (5 cm is sufficient).
• It is important that you release the cart from the same position for each trial.
• Record the distance along the ramp from the front of the cart at the release point to the rubber bumper at the end. Beware the gap in the yellow measuring tape on the ramps.
• Measure with a stopwatch the time T it takes for the cart to roll down the slope. Even though the stopwatch will display times with two decimal places, this level of precision (0.01 seconds) is unattainable by the human using the stopwatch. Suggest a more reasonable timing measurement error, T.
• Repeat a sufficient number of times (you decide how many).

## Error analysis

### Part 1

• Find your reaction time and its propagated error: t ± t.
• Identify at least two sources of statistical error.
• Identify at least two sources of systematic error.

### Part 2

• Find the acceleration of the cart and its propagated error: a ± a.
• Identify at least two sources of statistical error.
• Identify at least two sources of systematic error.

Back to the Mechanics Manual