6.3 Investigating Movement Using a Motion Detector
A CBR is a motion detector. The letters stand for Computer Based Ranger. It connects to a TI83+ calculator and it produces a graph of the movement of an object in front of it.
A sample graph is shown here. The horizontal axis is time
in seconds. The vertical axis is distance in metres.
You can calculate the speed of a line segment by calculating
∆𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
∆𝑡𝑖𝑚𝑒
.
Definitions

On a graph, the speed is given by the _________________ of the line segment.

If the line segment is __________________, then the speed is constant.

If the line segment is __________________, then the speed is changing.

An upward curve means the speed is increasing (_____________________), while a
downward curve means the speed is decreasing (_______________________).

The less steep the line is, the ________________ the speed.

The steeper the line is, the ________________ the speed.

If the line is _________________________, then the person is not moving.

If you move ____________________ the motion sensor, the line slopes DOWN to the right.

If you move _____________________ from the motion sensor, the line slopes UP to the
right.

The y-intercept tells us where the person ____________________ their walk.
1. Fill in the blanks for the following screen shot.
The person started ______ m from the CBR.
The person started walking ____________ from the CBR and
then at ____________ the person walked
______________ the CBR.
The person walked away from the CBR at a _______________ speed of ____________.
The person walked towards the CBR at a ________________ speed of ____________.
The person walked away from the CBR at a _________________ speed than the person walked
towards the CBR, because the first segment is _____________________.
The total time taken for the trip was ____________.
The total distance travelled was ______________.
2. Draw a graph to match the following descriptions.
a) A person starts 0.5 m away from the CBR
and runs away from the CBR at a constant
speed of2 m/s. At 2 s the person walks away
from the CBR at a constant speed of 0.5 m/s.
At 4 s the person runs towards the CBR at a
constant speed of 3 m/s for 1 s.
b) A person stands still for 3 seconds. 5
metres away from the CBR. Then the person
quickly increases his speed as he moves all
the way to the CBR. The entire sequence
lasted for 7 s.
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
8
9
The total distance travelled was _______
0
1
2
3
4
5
6
7
8
9
The total distance travelled was _______
Exercises:
1. Draw a graph to match the following descriptions.
a) A person starts 4 metres from the CBR and
walks at a constant pace of 1 m/s towards the
CBR for 3 seconds. The person stands still for
2 seconds and then runs back to the starting
position. The total trip took 6 seconds.
b) A person begins 0.5 metres from the
CBR and moves for 3 seconds at a
constant speed away from the CBR. Then
the person gradually slows down until he
comes to a complete stop 5 m away from the
motion detector. The total trip took 9
seconds.
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
8
0
9
c) A person stands still for 2 seconds, 3
metres away from the CBR. Then the person
walks towards the CBR gradually increasing
his speed.
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
d) A person starts 5 metres away from the
CBR and moves towards the CBR at a
decreasing speed for 3 s. The person is then
1 metre from the CBR. Then the person
walks away from the CBR at a constant
speed for 2 s. Finally, the person runs away
from the CBR at a constant speed for 1
second.
6
0
1
0
1
2
3
4
5
6
7
8
9