# Motion in One Dimension Worksheet 4

```Name
Period
Date
Motion in One Dimension Worksheet 4
Steel
Sphere
D
Recording
Plate
2006 AP B (Modified)
A student wishing to determine experimentally the acceleration g due to gravity has
an apparatus that holds a small steel sphere above a recording plate, as shown above.
When the sphere is released, a timer automatically begins recording the time of fall.
The timer automatically stops when the sphere strikes the recording plate. The student
measures the time of fall for different values of the distance D shown above and records
the data in the table below.
Distance of Fall (m)
Time of Fall (s)
0.10
0.14
0.50
0.32
1.00
0.46
1.70
0.59
Distance (m)
Time (s)
a. On the grid above, plot Distance vs. Time, including scaling the axis.
b. Sketch the smooth curve that best represents the student’s data.
2.00
0.63
Motion in One Dimension – WS 4
page 2
The student can use these data for distance D and time t to produce a second graph
from which the acceleration g due to gravity can be determined.
c. If only the variables D and t are used, what quantities should the student graph in
order to produce a linear relationship between the two quantities?
d. Calculate values for any of the quantities identified in (c) that are not given in the
data, and record these values in the table above. Label the row heading,
including units.
e. On the grid below, plot the data points for the quantities you have identified in
part (c), and sketch the best straight-line fit to the points. Label your axis
including units and show the scale that you have chosen for the graph.
f. Using the slope of your graph in part (e), calculate the acceleration g due to
gravity in this experiment.
g. State one way in which the student could improve the accuracy of the results if
the experiment were to be performed again. Explain why this would improve the
accuracy.
Motion in One Dimension – WS 4
page 3
Problem 2
The fan cart shown above is released from rest and allowed to move across a
horizontal floor. A student measures the position of the fan cart at various times and
records the data in the table below.
Position
(m)
Time
(s)
0.12
0.50
0.86
1.62
2.70
3.50
0.50
1.00
1.50
2.00
2.50
3.00
a. If only the variables position and time are used, what quantities should the student
graph in order to produce a linear relationship between the two quantities?
b. Calculate values for any of the quantities identified in (a) that are not given in the
data, and record these values in the table above. Label the row heading,
including units.
Motion in One Dimension – WS 4
page 4
c. On the axis below, plot the quantities you indicated in (a). Label the axis with the
variables, units and appropriate numbers to indicate the scale.
d. Sketch a best-fit straight line through the data.
e. Using information from the graph, create an equation that describes the position
of the fan cart as a function of time.
f. Calculate the acceleration of the fan cart.
```