Position and Velocity Measurements

Figure 1

Motion is best described by a position vs. time graph. From this graph one can derive velocity.

Velocity, v, is defined as the rate of change of the position of an object. The average velocity, đ?œˆĚ… , can be calculated as:

đ?œˆĚ… =

Δ� Δ�

Where: Δx = The displacement Δt = The time elapsed In this experiment we will use the Distance sensor to monitor the motion of a ball.

einstein™Tablet+ with MiLAB or Android/iOS Tablet with MiLAB and einstein™LabMate Distance sensor Distance adaptor Basketball or other round ball

(1)

1.

Launch MiLAB (

2.

Connect the Distance sensor with the Distance adaptor to one of the ports on the einstein™Tablet+ or einstein™LabMate.

Make sure only the Distance sensor is selected.

3.

).

Program the sensors to log data according to the following setup: Distance sensor

Distance (outgoing) (m)

Rate:

25/sec

Duration:

2 Min

1.

2.

Place the Distance sensor on the floor or a smooth, flat surface where you can roll a basketball for several meters (see Figure 1).

Place the ball on the floor half a meter from the Distance sensor.

3.

Tap Run (

4.

Roll the ball across the floor, away from the Distance sensor, by giving it a gentle push.

5.

When the ball reaches the end of the track or a distance of 10 m, tap Stop (

6.

Save your data by tapping Save (

) on the upper toolbar to begin recording data. ).

) on the upper toolbar.

For more information on working with graphs see: Working with Graphs in MiLAB. Look at the graph and answer the following questions: 1. Does the slope of the graph change over time?

2. Use Equation (1) to calculate the average velocity of the ball over three different time intervals.

How does the speed change during those intervals?

3. Place a cursor on the plot line.

4.

Tap the Function button (

).

5.

Select Derivative from the Mathematical Functions menu to calculate a velocity vs time graph. Discuss the graph.

6. Compare the results to the velocities you calculated using Equation (1).