Objective:
The main objective of this lab is to examine the various types of motion of an object in a
one-dimensional motion by tracking the changes of position and velocity of the object in
comparison to time. The characteristics of linear motion is determined by comparing the
position vs time data from the velocity vs time data through one instance without the
acceleration of gravity and one with the acceleration of gravity taken into account.
Experimental Data:
T1. Constant Velocity Motion.
TABLE 1
Way of moving Slope ± uncertainty, Statistics value
(position vs time graph) (velocity vs time graph)
Toward to the motion sensor -0.710 ± 0.0015 -0.710
Away from the motion sensor 0.424 ± 7.6x10-4 0.420
Experiment 2. Uniformly Accelerated Motion
TABLE 2 (Position vs Time)
Run # A (Value ± uncertainty) B (Value ± uncertainty) C (Value ± uncertainty)
(acceleration divided by 2) (initial velocity) (initial position)
Run up the 0.201 ± 0.0011 -0.757 ± 0.0020 1.07 ± 7.7x10-4
track
Run down 0.181 ± 0.0020 -0.019 ± 0.0047 0.208 ± 0.0024
the track
, TABLE 3 (Velocity vs Time)
Run # Slope Value ± uncertainty Y intercept ± uncertainty
Run up the track 0.422 ± 0.0018 -0.779 ± 0.0027
Run down the track 0.370 ± 0.0018 -0.0277 ± 0.0022
Data Analysis:
Experiment 1:
Position as a function of time Equation: x = v0t + (½)at2
(position) = (initial velocity)*(time) + (½)(acceleration)(time)2
Toward Sensor: x = (-0.710)t + (½)(0)t2
Since the velocity is constant the acceleration is zero
Away from Sensor: x = (0.424)t + (½)(0)2
Since the velocity is constant the acceleration is zero
Experiment 2:
(Run up the Track Acceleration) = (Slope of Velocity vs Time) divided by 2
0.201 ≈ 0.422/2
(Run down the Track Acceleration) = (Slope of Velocity vs Time) divided by 2
0.181 ≈ 0.370/2
Position as a function of time Equation: x = x0 + v0t + (½)at2
(position) = (initial position) + (initial velocity)*(time) + (½)(acceleration)(time)2
Up the Track: x = (1.07) + (-0.757)t + (½)(0.422)t2
Down the Track: x = (0.208) + (-0.019)t + (½)(0.370)2
The main objective of this lab is to examine the various types of motion of an object in a
one-dimensional motion by tracking the changes of position and velocity of the object in
comparison to time. The characteristics of linear motion is determined by comparing the
position vs time data from the velocity vs time data through one instance without the
acceleration of gravity and one with the acceleration of gravity taken into account.
Experimental Data:
T1. Constant Velocity Motion.
TABLE 1
Way of moving Slope ± uncertainty, Statistics value
(position vs time graph) (velocity vs time graph)
Toward to the motion sensor -0.710 ± 0.0015 -0.710
Away from the motion sensor 0.424 ± 7.6x10-4 0.420
Experiment 2. Uniformly Accelerated Motion
TABLE 2 (Position vs Time)
Run # A (Value ± uncertainty) B (Value ± uncertainty) C (Value ± uncertainty)
(acceleration divided by 2) (initial velocity) (initial position)
Run up the 0.201 ± 0.0011 -0.757 ± 0.0020 1.07 ± 7.7x10-4
track
Run down 0.181 ± 0.0020 -0.019 ± 0.0047 0.208 ± 0.0024
the track
, TABLE 3 (Velocity vs Time)
Run # Slope Value ± uncertainty Y intercept ± uncertainty
Run up the track 0.422 ± 0.0018 -0.779 ± 0.0027
Run down the track 0.370 ± 0.0018 -0.0277 ± 0.0022
Data Analysis:
Experiment 1:
Position as a function of time Equation: x = v0t + (½)at2
(position) = (initial velocity)*(time) + (½)(acceleration)(time)2
Toward Sensor: x = (-0.710)t + (½)(0)t2
Since the velocity is constant the acceleration is zero
Away from Sensor: x = (0.424)t + (½)(0)2
Since the velocity is constant the acceleration is zero
Experiment 2:
(Run up the Track Acceleration) = (Slope of Velocity vs Time) divided by 2
0.201 ≈ 0.422/2
(Run down the Track Acceleration) = (Slope of Velocity vs Time) divided by 2
0.181 ≈ 0.370/2
Position as a function of time Equation: x = x0 + v0t + (½)at2
(position) = (initial position) + (initial velocity)*(time) + (½)(acceleration)(time)2
Up the Track: x = (1.07) + (-0.757)t + (½)(0.422)t2
Down the Track: x = (0.208) + (-0.019)t + (½)(0.370)2
