Measurement No. time t (s) distance x (m) 1 0.300 1.59E-02 (i.e. 1.59 × 10−2) 2 0.500 4.31E-02 3 0.700 9.04E-02 4 1.20 2.70E-01 Questions Plot x vs. t on log-log paper. Label all axes properly, and draw a best-fit line through the data points. Determine the slope of the best-fit line. Based on the slope, what type of motion does the mass do? Now assume that the motion is described by From the given values for t and x, calculate the acceleration a for each measurement and write it down in a table. Be sure to add the proper unit. For the acceleration, find the average, the standard deviation, standard deviation of the mean and 2σ-uncertainty. Report the final answer in standard form (mean ± uncertainty) with proper rounding and units.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Using video analysis, the motion of an object has been recorded as follows:
| Measurement No. | time t (s) | distance x (m) |
| 1 | 0.300 | 1.59E-02 (i.e. 1.59 × 10−2) |
| 2 | 0.500 | 4.31E-02 |
| 3 | 0.700 | 9.04E-02 |
| 4 | 1.20 | 2.70E-01 |
Questions
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Plot x vs. t on log-log paper. Label all axes properly, and draw a best-fit line through the data points.
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Determine the slope of the best-fit line. Based on the slope, what type of motion does the mass do?
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Now assume that the motion is described by
From the given values for t and x, calculate the acceleration a for each measurement and write it down in a table. Be sure to add the proper unit. -
For the acceleration, find the average, the standard deviation, standard deviation of the mean and 2σ-uncertainty.
Report the final answer in standard form (mean ± uncertainty) with proper rounding and units.
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