81
-5
0
5
0.511.5
t (s)
1
2
a =
-
10 m/s2a =
-
10 m/s2a =
-
10 m/s2
Section 3.3Positive and Negative Acceleration
Discussion questions
A. What is wrong with the following definitions of g.
(a) “g is gravity.”
(b) “g is the speed of a falling object.”
(c) “g is how hard gravity pulls on things.”
B. When advertisers specify how much acceleration a car is capable of, they
do not give an acceleration as defined in physics. Instead, they usually specify
how many seconds are required for the car to go from rest to 60 miles/hour.
Suppose we use the notation “a” for the acceleration as defined in physics,
and “a
car ad
” for the quantity used in advertisements for cars. In the US’s non-
metric system of units, what would be the units of a and a
car ad
. How would the
use and interpretation of large and small, positive and negative values be
different for a as opposed to a
car ad
.
C. Two people stand on the edge of a cliff. As they lean over the edge, one
person throws a rock down, while the other throws one straight up with an
exactly opposite initial velocity. Compare the speeds of the rocks on impact at
the bottom of the cliff.
3.3Positive and Negative Acceleration
Gravity always pulls down, but that does not mean it always speeds
things up. If you throw a ball straight up, gravity will first slow it down to
v=0 and then begin increasing its speed. When I took physics in high
school, I got the impression that positive signs of acceleration indicated
speeding up, while negative accelerations represented slowing down, i.e.
deceleration. Such a definition would be inconvenient, however, because we
would then have to say that the same downward tug of gravity could
produce either a positive or a negative acceleration. As we will see in the
following example, such a definition also would not be the same as the slope
of the v-t graph
Let’s study the example of the rising and falling ball. In the example of
the person falling from a bridge, I assumed positive velocity values without
calling attention to it, which meant I was assuming a coordinate system
whose x axis pointed down. In this example, where the ball is reversing
direction, it is not possible to avoid negative velocities by a tricky choice of
axis, so let’s make the more natural choice of an axis pointing up. The ball’s
velocity will initially be a positive number, because it is heading up, in the
same direction as the x axis, but on the way back down, it will be a negative
number. As shown in the figure, the v-t graph does not do anything special
at the top of the ball’s flight, where v equals 0. Its slope is always negative.
In the left half of the graph, the negative slope indicates a positive velocity
that is getting closer to zero. On the right side, the negative slope is due to a
negative velocity that is getting farther from zero, so we say that the ball is
speeding up, but its velocity is decreasing!
To summarize, what makes the most sense is to stick with the original
definition of acceleration as the slope of the v-t graph,
.
v/
.
t. By this
definition, it just isn’t necessarily true that things speeding up have positive
acceleration while things slowing down have negative acceleration. The
word “deceleration” is not used much by physicists, and the word “accelera-
tion” is used unblushingly to refer to slowing down as well as speeding up:
“There was a red light, and we accelerated to a stop.”
Example
Question: In the example above, what happens if you calculate