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2.5Addition of Velocities
Addition of velocities to describe relative motion
Since absolute motion cannot be unambiguously measured, the only
way to describe motion unambiguously is to describe the motion of one
object relative to another. Symbolically, we can write v
PQ
for the velocity of
object P relative to object Q.
Velocities measured with respect to different reference points can be
compared by addition. In the figure below, the ballís velocity relative to the
couch equals the ballís velocity relative to the truck plus the truckís velocity
relative to the couch:
v
BC
=
v
BT
+v
TC
= 5 cm/s + 10 cm/s
The same equation can be used for any combination of three objects, just
by substituting the relevant subscripts for B, T, and C. Just remember to
write the equation so that the velocities being added have the same sub-
script twice in a row. In this example, if you read off the subscripts going
from left to right, you get BC...=...BTTC. The fact that the two ďinsideĒ
subscripts on the right are the same means that the equation has been set up
correctly. Notice how subscripts on the left look just like the subscripts on
the right, but with the two Tís eliminated.
These two highly competent physicists disagree on absolute velocities, but they would agree on relative
velocities. Purple Dino considers the couch to be at rest, while Green Dino thinks of the truck as being at rest.
They agree, however, that the truckís velocity relative to the couch is v
TC
=10 cm/s, the ballís velocity relative
to the truck is v
BT
=5 cm/s, and the ballís velocity relative to the couch is v
BC
=v
BT
+v
TC
=15 cm/s.
In one second, Green Dino and the
truck both moved forward 10 cm, so their
velocity was 10 cm/s. The ball moved
forward 15 cm, so it had v=15 cm/s.
Purple Dino and the couch both
moved backward 10 cm in 1 s, so they
had a velocity of -10 cm/s. During the same
period of time, the ball got 5 cm closer to
me, so it was going +5 cm/s.
Section 2.5Addition of Velocities
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