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Vertical motion
Average velocity
In order to deal with the velocity of the metal ball
during its motion, we measure the height at a few more instants.
The result is shown in the table below.
|
time (s)
|
0.0
|
0.1
|
0.2
|
0.3
|
0.4
|
0.5
|
0.6
|
0.7
|
0.8
|
0.9
|
|
height (m)
|
0.0
|
1.95
|
3.80
|
5.56
|
7.21
|
8.77
|
10.23
|
11.60
|
12.86
|
14.03
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
1.0
|
1.1
|
1.2
|
1.3
|
1.4
|
1.5
|
1.6
|
1.7
|
1.8
|
1.9
|
|
height (m)
|
15.10
|
16.07
|
16.94
|
17.72
|
18.39
|
18.97
|
19.45
|
19.84
|
20.12
|
20.31
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
2.0
|
2.1
|
2.2
|
2.3
|
2.4
|
2.5
|
2.6
|
2.7
|
2.8
|
2.9
|
|
height (m)
|
20.40
|
20.39
|
20.28
|
20.07
|
19.77
|
19.37
|
18.87
|
18.27
|
17.58
|
16.78
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
3.0
|
3.1
|
3.2
|
3.3
|
3.4
|
3.5
|
3.6
|
3.7
|
3.8
|
3.9
|
|
height (m)
|
15.89
|
14.90
|
13.81
|
12.63
|
11.34
|
9.96
|
8.48
|
6.91
|
5.23
|
3.46
|
| |
|
|
|
|
|
|
|
|
|
|
|
time (s)
|
4.0
|
4.08
|
|
|
|
|
|
|
|
|
|
height (m)
|
1.58
|
0.0
|
|
|
|
|
|
|
|
|
A graphical representation for the table can be found
here
Using the values of the above table,
we determine the average velocity in each time interval.
For example, in the interval of time which runs
from the instant 3.0 s
to the instant 3.1 s,
the metal ball falls
from a height of 15.89 m
to a height of 14.90 m.
Hence its displacement equals -0.99 m
in a time interval of 0.1 s.
Consequently, its average velocity in that time interval
equals -9.9 m/s
(negative, because the ball moves downward
in the interval under consideration).
The values obtained for all intervals are collected
in the table below.
|
interval (s)
|
average
velocity (m/s)
|
|
0.0 - 0.1
|
19.5
|
|
0.1 - 0.2
|
18.5
|
|
0.2 - 0.3
|
17.6
|
|
0.3 - 0.4
|
16.5
|
|
0.4 - 0.5
|
15.6
|
|
0.5 - 0.6
|
14.6
|
|
0.6 - 0.7
|
13.7
|
|
0.7 - 0.8
|
12.6
|
|
0.8 - 0.9
|
11.7
|
|
0.9 - 1.0
|
10.7
|
|
1.0 - 1.1
|
9.7
|
|
1.1 - 1.2
|
8.7
|
|
1.2 - 1.3
|
7.8
|
|
1.3 - 1.4
|
6.7
|
|
1.4 - 1.5
|
5.8
|
|
1.5 - 1.6
|
4.8
|
|
1.6 - 1.7
|
3.9
|
|
1.7 - 1.8
|
2.8
|
|
1.8 - 1.9
|
1.9
|
|
1.9 - 2.0
|
0.9
|
|
2.0 - 2.1
|
-0.1
|
|
2.1 - 2.2
|
-1.1
|
|
2.2 - 2.3
|
-2.1
|
|
2.3 - 2.4
|
-3.0
|
|
2.4 - 2.5
|
-4.0
|
|
2.5 - 2.6
|
-5.0
|
|
2.6 - 2.7
|
-6.0
|
|
2.7 - 2.8
|
-6.9
|
|
2.8 - 2.9
|
-8.0
|
|
2.9 - 3.0
|
-8.9
|
|
3.0 - 3.1
|
-9.9
|
|
3.1 - 3.2
|
-10.9
|
|
3.2 - 3.3
|
-11.8
|
|
3.3 - 3.4
|
-12.9
|
|
3.4 - 3.5
|
-13.8
|
|
3.5 - 3.6
|
-14.8
|
|
3.6 - 3.7
|
-15.7
|
|
3.7 - 3.8
|
-16.8
|
|
3.8 - 3.9
|
-17.7
|
|
3.9 - 4.0
|
-18.8
|
|
4.0 - 4.08
|
-19.8
|
A graphical representation for the table can be found
here
Observe that the average velocity decreases on average
about 1 m/s
in each subsequent interval.
A more precise average of the decrease in velocity
can be obtained by averaging over all intervals.
The result equals a decrease of 0.98 m/s
in each 0.1 second.
Which gives a deceleration of 9.8 m/s
per second, which is in agreement with the previous result
for the acelleration of gravity.
Most important is the conclusion that
the acelleration a
of the metal ball is constant and negative
and, moreover,
equal to the gravitational
acelleration g,
which is expressed by the relation
a = - g
different object