reading assignment: (3.1) what is this vector indicating? a.a velocity with a 1.5 cm component b.a...
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Reading Assignment: (3.1)
What is this vector indicating?
ˆˆ3.0 4.5r cm cm j
A. A velocity with a 1.5 cm component
B. A displacement with a 1.5 cm component
C. A displacement vector with the components (3.0 cm, 4.5 cm)
D. A position vector to a place at (3.0 cm. 4.5 cm)
In a dance, you are standing in a spot, and your partner is
located 5 steps to the right of you. He takes 5 steps
back, 10 steps to his left. Which displacement does he
need to undergo to end up beside you?
Draw the picture for the following problem, label, and write an appropriate vector equation:
Short exercise
You are observing deer. First, you spot the
buck 200m at NNE. A few seconds later,
he surfaces again north of you. From the
time that has passed you determine that
the buck can not have further than 80 m
away from the first position. What is the
buck’s new position vector?
Draw the picture for the following problem, label, and write an appropriate vector equation:
Short exercise
Refinement for average velocity
observerdefines reference point
Position vector 1r
Time t1
Position vector 2r
Time t2
Displacement vector r
2 1r r r
1
2 1
2ave
r rv
t t
r
t
Average velocity: change in position over time
Position vectors: bound to a reference point
You watch a ground hog poke his head out of a
hole 20m due North of your position. About 15 s
later, he appears at a distance of 45 m West of
you.
a)Determine its displacement.
b)Determine its average velocity.
Instantaneous velocity
1r
2r
r
Direction of average velocity?
avev
ave
rv
t
Strategy: bring the two points closer together.
Instantaneous velocity
1r
2r
r avev
ave
rv
t
Instantaneous velocity
1r
2r
r dr
1 becomes at position avev v r
ave
rv
t
0limt
r drv
t dt
Velocity vector?
vxv
yvˆ ˆx yv v i v j
Speed?2 2x yv v v
What are those components?
x
dxv
dt
y
dyv
dt
Average acceleration
1r
2r
1v
ave
va
t
Change in velocity?
2v
1v
2v
2 1v v v
Rate of change in velocity?
Average acceleration is the averagerate of change in instantaneous velocity.
Instantaneous acceleration
r t
( )v t
Change in velocity?
dv v t dt v t
0Instantaneous acceleration lim
t
v dva
t dt
xx
dva
dt y
y
dva
dt
r t dt
v t dt
( )v t
v t dt
Reading Assignment: (3.2)
Which of the particles below has zero acceleration?
A. A baseball is flying beyond the playing field for a
home run.
B. A child in a Ferris Wheel being spun around at
constant speed.
C.A glider is sliding off an inclined air track.
D.A car is slowing down on an icy straight road.
A ship’s echo on a radar screen ismoving according to
in which all lengths are in km and times in hours.
a) Find the position at time zero, after 30 min and after 1 hour.b) Find the velocity as a function of time; then calculate it at time
zero, 30 min and 1h.c) Find the acceleration as a function of time; then calculate the
acceleration at zero. 30 min and 1 h.d) Draw positions into an x-y coordinate system, and indicate the
respective velocity and acceleration vectors.
2 ˆˆ10 4 25 25r t t t j
Example
A toy train is traveling around a circular track. Its position changes with time as
a)Find the position of the train after 5 s.
b)Find the velocity of the train after 5 s.
x
y
ˆ ˆ1.00 cos 2 1.00 sin 210 10
t tr t m i m j
s s