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