PART II- REVERSING OURSELVES!

REMEMBER THAT THE SLOPE OF A POSITION, TIME GRAPH PRODUCES
VELOCITY!

ALSO, REMEMBER THAT THE SLOPE OF A VELOCITY, TIME GRAPH
PRODUCES ACCELERATION!

HOW COULD WE GO "BACK" FROM A VELOCITY, TIME GRAPH TO A
POSITION, TIME GRAPH?

A RATIO FROM EACH OF OUR GRAPHS CONNECTS TO THE
GEOMETRIC CONCEPT OF SLOPE.

IN A SIMILAR FASHION, A PRODUCT CONNECTS TO THE
GEOMETRIC CONCEPT OF AREA.

SINCE D X = V DT (A PRODUCT), THE AREA BETWEEN THE
VELOCITY GRAPH AND THE TIME AXIS GIVES US POSITION.

Look at this velocity graph
once again. The average
velocity equals the average of
the smallest (0 m/s) and the
largest (12 m/s). The average
velocity is 6 m/s. Multiply the
average velocity by the time.
The position gained from a
zero starting point will be
calculated from this product. A
value of 48 meters is found.
Now look at the calculation a
different way. What we did was,
in effect, take the average
height or

(1/2) [h1 + h2] = 6 m/s

and multiply it by the base of 8 s
to obtain the position.

THE AREA OF A VELOCITY, TIME GRAPH GIVES
POSITION. THE AREA OF AN ACCELERATION, TIME
GRAPH GIVES VELOCITY.

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TRY THIS KINEMATICS
CROSSWORD PUZZLE

QUESTIONS:

1. The product of velocity (vertical
axis) and time (horizontal axis)
produces _____.

2. Wjat is the unit on this product?

3. What is the value of the area
(position) from 0 to 1 s?

4. Is the area from 3 to 4 s positive
or negative?

5. What is the final position (total
area) from 0 to 4 s?

Place MOUSE over jumbled letters below for answers!