Constant Acceleration and
Relative Velocity
Relative Velocity

Sometimes your velocity is known relative to a
reference frame that is moving relative to the
earth.
Example 1: A person moving relative to a train, which
is moving relative to the ground.
Example 2: a plane moving relative to air, which is
then moving relative to the ground.

These velocities are related by vector addition:



vac  vab  v bc
» vac is the velocity of the object relative to
the ground
» vab is the velocity of the object relative to
a moving reference frame
» vbc is the velocity of the moving reference
frame relative to the ground
Physics 101: Lecture 6, Pg 2
32
Relative Velocity
You are on a train traveling 40 mph North. If
you walk 5 mph toward the front of the
train, what is your speed relative to the
ground?
A) 45 mph
40
45
B) 40 mph
C) 35 mph
5
25
Relative Velocity
You are on a train traveling 40 mph North. If
you walk 5 mph toward the rear of the train,
what is your speed relative to the ground?
A) 45 mph
40
35
B) 40 mph
C) 35 mph
5
27
Relative Velocity
You are on a train traveling 40 mph North. If
you walk 5 mph sideways across the car,
what is your speed relative to the ground?
A) < 40 mph
B) 40 mph
C) >40 mph
40 mph N + 5 mph W =
5
40
30
Example: airplane
•An airplane needs to fly due south to
reach it’s destination, but there is a wind
blowing from the east. Will this increase,
decrease or have no effect on the travel
time?
vp= 50 m/s
vT
vw= 20 m/s
Example
y
x
Three swimmers can swim equally fast relative to the water. They
have a race to see who can swim across a river in the least time.
Relative to the water, Beth (B) swims perpendicular to the flow,
Ann (A) swims upstream, and Carly (C) swims downstream. Which
swimmer wins the race?
A) Ann
B) Beth
C) Carly
correct
A B C
39
y
Example
x
If the width of the river is 50m and Beth can swim at 3m/s, how
long does it take her to get across? If the river is flowing at
2m/s, How far downstream is she swept?
50m
A B C
2m/s
39
y
Swimmer Example
x
What angle should Ann take to get directly to the other side if
she can swim 3 mph relative to the water, and the river is
flowing at 2 mph?
How long does it take her to get across?
q
A B C
2m/s
48
Summary of Concepts
X
and Y directions are Independent!
Position, velocity and acceleration are vectors
F
= m a applies in both x and y direction
 Relative
Motion (Add vector components)



vsg  vsw  v wg