Purpose: The purpose of this lab is to compare method used to

find average velocity and instantaneous velocity, and to apply a limit to the instantaneous velocity to compare graphically.

Background: Average velocity is a measure of displacement in a given

period of time; it is ratio of displacement per time. Instantaneous velocity is the first derivative of position.

Materials: Xplorer GLX PASCO PASCO PAS Track Tape (3) Textbooks (2) PASCO Photogates PASCar

Piece of paper (to mount as a flag in the middle of the racecar)

Stand mounts Ruler Digital Adapter

Procedure:

Part 1 – Measure Average Velocity on Upper End of Ramp

1) Elevate ramp by stacking the textbooks.2) Clamp photogates on the stand mounts.3) Set up photogates at 20 cm AND 50 cm.4) Set up Xplorer GLX PASCO so that the TIME BETWEEN GATES is

set to “VISIBLE.”5) Release the racecar at the top of the ramp.6) Record the time elapsed between photogates.7) Reset the screen and clear the time.8) Repeat Steps 5-7 for (3) trials.

Part 2 – Measure Average Velocity on Middle Section of Ramp

1) Set up photogates at 35 cm AND 65 cm.2) Release the racecar at the top of the ramp.3) Record the time elapsed between photogates.4) Reset the screen and clear the time.5) Repeat Steps 2-4 for (3) trials.

Part 3 – Measure Average Velocity on Lower Section of Ramp

1) Set up photogates at 60 cm AND 90 cm.2) Release the racecar at the top of the ramp.3) Record the time elapsed between photogates.4) Reset the screen and clear the time.5) Repeat Steps 2-4 for (3) trials.

Part 4 – Measure Average Velocity of Entire Ramp1) Set up photogates at 20 cm AND 90 cm.2) Release the racecar at the top of the ramp.3) Record the time elapsed between photogates.4) Reset the screen and clear the time.5) Repeat Steps 2-4 for (3) trials.

Data:

(2) photogates: Trial Top (20-

50cm)Middle (35-65cm)

Bottom (60-90cm)

Total (20-90cm)

1 0.4590s 0.3453s 0.2531s 0.7850s2 0.4395s 0.3407s 0.2696s 0.7842s3 0.4500s 0.3463s 0.2666s 0.8339sAvg. Time 0.4495s 0.3441s 0.2631s 0.8010sVelocity (dist./time)

0.6670 m/s

0.8720 m/s

1.140 m/s 0.8740 m/s

Average of Top, Middle, and Bottom Velocities: 0.893 m/s

(1)photogate: Trial Whole ½ ¼ 1/8

1 0.1402s 0.0707s 0.0343s 0.0164s2 0.1399s 0.0709s 0.0344s 0.0165s3 0.1403s 0.0701s 0.0345s 0.0163sAverage 0.1401s 0.0706s 0.0344s 0.0164sVelocity (dist./time)

0.906 m/s 0.907 m/s 0.930 m/s 0.977 m/s

Distances Whole ½ ¼ 1/80.127m 0.064m 0.032m 0.016m

Analysis/Observations:The speed at the bottom of the ramp was the greatest.Percent Error: [(0.893 – 0.8740)/0.8740] X 100 = 2.17%

Conclusion:The average velocity was experimentally determined by

averaging the velocity of the three regions of the track. Each of these velocities was calculated by dividing the displacement by the change in time.

Instantaneous velocity was experimentally calculated by averaging the speed of the racecar at a particular point on the track, 50cm.

Juxtaposing the average velocity with the instantaneous velocity reveals that the instantaneous velocity is more accurate because it factors the velocity of several regions of the track.