Here is another falling body problem. The object is a toy car being pushed up a ramp and allowed to slow, stop, and roll down the ramp. The sensor is place at the top of the ramp "looking" down. See the results for a different experiment, a frisbee being dropped on the CBL.

The Smoothed Data
0 < t (s) < 4
0 < d (m) < 2
Distance vs. Time
.9 < t (s) < 1.7
0 < d (m) < 1

Here is the raw data after it has been smoothed. The first maximum is a part of the push that the toy car received. The graph flattens after the object has reached its closest point to the sensor and then accelerated down the ramp.

Here is the position of our object during the acceleration as a function of time. It is what we would expect, resembling a parabola. This is only a portion of the original raw data.

Velocity vs. Time
.9 < t s) < 1.7
-1 < v (m/s) < 2
Acceleration vs. Time
.9 < t (s) < 1.7
0 < a (m/s/s) < 4

Here is the velocity vs. time graph. Notice that the object's velocity is going more and more positive as it accelerates away from the sensor. The pattern resembles the equation V(t)=Vo+at. Notice the change in the character of the velocity graph when V=0. Think about which direction friction is working.

Here is the acceleration vs. time graph. Notice that it is always positive and fairly constant because the object is accelerating away from the sensor. The average acceleration here is 2.25 m/s/s. The theoretical average given the angle of the ramp should be 2.88 m/s/s.


A small calculator program can be written to use the TI STAT-CALC functions in order to fit the data the Position vs. Time graph. For this trial, the equation is:

d=-9.501t^2+4.479t+5.037

How does this compare with the theoretical equation for falling bodies in one dimension?