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Discussion question B.
Section 3.3Positive and Negative Acceleration
Because the positive and negative signs of acceleration depend on the
choice of a coordinate system, the acceleration of an object under the
influence of gravity can be either positive or negative. Rather than having to
write things like “g=9.8 m/s
2
or -9.8 m/s
2
” every time we want to discuss g’s
numerical value, we simply define g as the absolute value of the acceleration
of objects moving under the influence of gravity. We consistently let g=9.8
m/s
2
, but we may have either a=g or a=-g, depending on our choice of a
coordinate system.
Example
Question: A person kicks a ball, which rolls up a sloping street,
comes to a halt, and rolls back down again. The ball has
constant acceleration. The ball is initially moving at a velocity of
4.0 m/s, and after 10.0 s it has returned to where it started. At the
end, it has sped back up to the same speed it had initially, but in
the opposite direction. What was its acceleration.
Solution: By giving a positive number for the initial velocity, the
statement of the question implies a coordinate axis that points up
the slope of the hill. The “same” speed in the opposite direction
should therefore be represented by a negative number, -4.0 m/s.
The acceleration is a=
.
v/
.
t=(v
after
-v
before
)/10.0 s=[(-4.0 m/s)-(4.0
m/s)]/10.0 s=-0.80 m/s
2
. The acceleration was no different during
the upward part of the roll than on the downward part of the roll.
Incorrect solution: Acceleration is
.
v/
.
t, and at the end it’s not
moving any faster or slower than when it started, so
.
v=0 and
a=0.
#
The velocity does change, from a positive number to a
negative number.
Discussion questions
A. A child repeatedly jumps up and down on a trampoline. Discuss the sign
and magnitude of his acceleration, including both the time when he is in the air
and the time when his feet are in contact with the trampoline.
B. Sally is on an amusement park ride which begins with her chair being
hoisted straight up a tower at a constant speed of 60 miles/hour. Despite stern
warnings from her father that he’ll take her home the next time she
misbehaves, she decides that as a scientific experiment she really needs to
release her corndog over the side as she’s on the way up. She does not throw
it. She simply sticks it out of the car, lets it go, and watches it against the
background of the sky, with no trees or buildings as reference points. What
does the corndog’s motion look like as observed by Sally. Does its speed ever
appear to her to be zero. What acceleration does she observe it to have: is it
ever positive. negative. zero. What would her enraged father answer if asked
for a similar description of its motion as it appears to him, standing on the
ground.
C. Can an object maintain a constant acceleration, but meanwhile reverse the
direction of its velocity.
D. Can an object have a velocity that is positive and increasing at the same
time that its acceleration is decreasing.
E. The four figures show a refugee from a Picasso painting blowing on a rolling
water bottle. In some cases the person’s blowing is speeding the bottle up, but
in others it is slowing it down. The arrow inside the bottle shows which