Uniform Acceleration Lab

Purpose: To determine the type of motion experienced by a cart rolling down an incline.

Theory: In this experiment, the type of motion that the cart is to experience while rolling down an incline is to be determined. This will be done by examining the cart’s position relative to the top of the ramp over a period of time.
Using the position of the cart over time, the displacement, velocity, and acceleration will be determined. A straight line on a position vs. time graph will represent uniform motion. A straight line on a velocity vs. time graph will represent uniform acceleration.
Position is the distance the object is from a point of reference, which includes a direction. Displacement is a change in an objects position, measured in cm. Velocity is a change in an objects position over time, measured in cm/s. Instantaneous velocity is a measure of the objects velocity at a specific time, calculated by the slope of a tangent at each specific time on the position vs. time graph. Acceleration is a change in an objects velocity over time, measured in m/s2, which can be found by calculating the slope of the line on the velocity vs. time graph. Uniform motion (uniform velocity) occurs when an object travels at a constant velocity (covers a constant displacement in a constant time). Uniform acceleration occurs when an object’s velocity is increasing at a constant rate.

Apparatus: Cart, ticker timer, 2.0 m ticker tape, masking tape, 2.0 m incline ramp, bricks/textbooks.

Figure 1: The apparatus

Procedure:
1) The apparatus was set up as shown above in figure 1; the top of the ramp was raised about 25 cm above the ground using textbooks.
2) The ticker tape was thread through the ticker timer and taped to the cart using masking tape.
3) The cart and ticker timer were placed at the top of the ramp.
4) The ticker timer was set to 60 Hz
5) The ticker timer was turned on as the cart was released from the top of the ramp.
6) The data was gathered from the ticker tape after the cart completed its run.
Observations and Calculations:

The following data was gathered from the ticker tape, which measured the position of the cart at each time interval.

Table 1: Ticker Tape Data

Time (s)
Position (cm [N])
Displacement (cm [N])
Average Velocity (cm/s [N])
Instantaneous Velocity (cm/s [N])
Acceleration (m/s2 [N])
0
0
0
0
0
0
0.1
0.9
0.9
9.0

0.9
0.2
2.7
1.9
19.0

1.00
0.3
4.8
2.0
20.0

0.10
0.4
7.9
3.1
31.0

1.70
0.5
13.1
5.2
52.0

1.50
0.6
20.5
7.4
74.0
83.3
2.20
0.7
30.1
9.6
96.0

2.20
0.8
41.7
11.6
116.0
120.0
2.00
0.9
55.2
13.5
135.0

1.90
1.0
70.5
15.3
153.0
166.7
1.80
1.1
87.7
17.2
172.0

1.90
1.2
107.1
19.4
194.0

2.20
1.3
128.3
21.2
212.0

1.80
1.4
151.6
23.3
233.0

2.10
1.5
176.3
24.7
247.0

1.40

The following graphs represent the position, velocity, and acceleration of the cart over time.

Calculations:

Discussion: The position vs. time graph showed an increasing, “cuppy” shape, which represents acceleration, this can be interpreted this way because the slope of the line is increasing as time passes, meaning that the cart is travelling faster and covering more distance in each time interval. The velocity vs. time graph showed an increasing straight line, which represents an increasing velocity and a constant acceleration. The slope of this line represents the average acceleration of the cart. The average velocity and instantaneous velocity values were