Definition of SpeedDefinition of Speed

• SpeedSpeed is the distance traveled per is the distance traveled per unit of time (a scalar quantity).unit of time (a scalar quantity).

• SpeedSpeed is the distance traveled per is the distance traveled per unit of time (a scalar quantity).unit of time (a scalar quantity).

v = = s

t

20 m

4 s

v = 5 m/sv = 5 m/s

Not direction dependent!

A

Bs = 20 m

Time t = 4 s

Definition of VelocityDefinition of Velocity

• VelocityVelocity is the displacement per is the displacement per unit of time. (A vector quantity.)unit of time. (A vector quantity.)

• VelocityVelocity is the displacement per is the displacement per unit of time. (A vector quantity.)unit of time. (A vector quantity.)

v = 3 m/s at 200 N of E

v = 3 m/s at 200 N of E

Direction required!

A

Bs = 20 m

Time t = 4 s

12 m

4 s

Dv

t

D=12 m

20o

Average Velocity and Average Velocity and Instantaneous VelocityInstantaneous Velocity

The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant. (v at point C)

The instantaneous velocity is the magn-itude and direction of the speed at a par-ticular instant. (v at point C)

The The averageaverage velocityvelocity depends depends ONLYONLY on on the displacement traveled and the time the displacement traveled and the time required.required.

The The averageaverage velocityvelocity depends depends ONLYONLY on on the displacement traveled and the time the displacement traveled and the time required.required.

A

Bs = 20 m

Time t = 4 s

C

Average and Average and Instantaneous Instantaneous vv

x

tt

xx

22

xx

11

tt22tt11

2 1

2 1avg

x x xv

t t t

2 1

2 1avg

x x xv

t t t

( 0)inst

xv t

t

( 0)inst

xv t

t

x

t

Time

slope

Dis

pla

cem

en

t,

x

Average Average Velocity:Velocity:

Instantaneous Instantaneous Velocity:Velocity:

Example 1.Example 1. A runner runs A runner runs 200 m, east,200 m, east, then changes direction and runs then changes direction and runs 300 m, 300 m, westwest. If the entire trip takes . If the entire trip takes 60 s60 s, what is , what is the average speed and what is the the average speed and what is the average velocity?average velocity?

Recall that Recall that average average speedspeed is a function is a function onlyonly of of total total distancedistance and and total total timetime::Total distance: Total distance: ss = 200 m + 300 m = 500 = 200 m + 300 m = 500 mm

500 m

60 s

total pathAverage speed

time Avg.

speed 8.33 m/s

Direction does not Direction does not matter!matter!

startstart

ss11 = 200 = 200 mm

ss22 = 300 = 300 mm

Example 1 (Cont.)Example 1 (Cont.) Now we find the Now we find the average velocity, which is the average velocity, which is the net net displacement displacement divided by divided by timetime. In this . In this case, the direction matters. case, the direction matters.

xxoo = 0 = 0

t t = 60 = 60 ssxx11= +200 = +200

mmxxff = -100 = -100 mm

0fx xv

t

xx00 = 0 m; x = 0 m; xff = -100 = -100 mm

100 m 01.67 m/s

60 sv

Direction of final Direction of final displacement is to displacement is to the left as shown.the left as shown.

Average velocity:

1.67 m/s, Westv

Note: Average velocity is directed to the Note: Average velocity is directed to the west.west.

Example 2.Example 2. A sky diver jumps and falls A sky diver jumps and falls for 600 m in 14 s. After chute opens, he for 600 m in 14 s. After chute opens, he falls another 400 m in 150 s. What is falls another 400 m in 150 s. What is average speed for entire fall?average speed for entire fall?

625 m

356 m

14 s

142 s

A

B

600 m + 400 m

14 s + 150 sA B

A B

x xv

t t

1000 m

164 sv 6.10 m/sv 6.10 m/sv

Average speed is a Average speed is a function function onlyonly of total of total distance traveled and the distance traveled and the total time required.total time required.

Average speed is a Average speed is a function function onlyonly of total of total distance traveled and the distance traveled and the total time required.total time required.

Total distance/ total time:Total distance/ total time:

Relative VelocityRelative Velocity

How fast?How fast?

It all depends on who you It all depends on who you ask!!ask!!

How fast?How fast?

It all depends on who you It all depends on who you ask!!ask!!

Relative VelocityRelative Velocity

•Velocity is a vector quantityVelocity is a vector quantity

•How it is measured depends on How it is measured depends on the frame of referencethe frame of reference

•The same motion can be The same motion can be described differently, based on described differently, based on the frame of referencethe frame of reference

Frame of ReferenceFrame of Reference

• When making measurements of When making measurements of the physical world, a reference the physical world, a reference point and directional system must point and directional system must be chosenbe chosen

• All measurements are made from All measurements are made from this reference point and within this reference point and within this directional systemthis directional system

• This frame of reference does not This frame of reference does not always have to be stationary…always have to be stationary…

Motions Motions Observed Observed from Different from Different Frames of Frames of ReferenceReference

Relative Velocity Relative Velocity Velocity of A relative to B:Velocity of A relative to B:

VVABAB==VVAA--VVB B

vvAB AB : v of A with respect to B: v of A with respect to B

vvB B : v of B with respect to a reference : v of B with respect to a reference frame (ex.: the ground)frame (ex.: the ground)

vvA A : v of A with respect to a: v of A with respect to a

reference frame (ex.: the ground) reference frame (ex.: the ground)

Example 1 Example 1

• The white speed boat has a velocity The white speed boat has a velocity of 30km/h,N, and the yellow boat a of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both with velocity of 25km/h, N, both with respect to the ground. What is the respect to the ground. What is the relative velocity of the white boat relative velocity of the white boat with respect to the yellow boat?with respect to the yellow boat?

• Answer: 5km/h, N Answer: 5km/h, N

Example 2- Example 2- The Bus Ride The Bus Ride

A passenger is seated on a bus that is A passenger is seated on a bus that is

traveling with a velocity of 5 m/s, North.traveling with a velocity of 5 m/s, North.

If the passenger remains in her seat,If the passenger remains in her seat,

what is her velocity: what is her velocity:

a)a) with respect to the ground? with respect to the ground?

b)b) with respect to the bus?with respect to the bus?

Relative Velocity in 2D

Constant velocity in each of two dimensions (example: boat & river, plane and wind)

Velocity of Boat in Still Water

Velocity of River

with respect to the ground

Adding vectors that are at 900 to each other. Draw the vector diagram and draw

the resultant. Use the Pythagorean Theorem to

calculate the resultant. Use θ=tan-1(y/x) to find the angle

between the horizontal and the resultant, to give the direction of the resultant. (00 is along the +x axis)

Example 4-Airplane and Wind

An airplane is traveling with a velocity of 50 m/s, E with respect to the wind. The wind is blowing with a velocity of 10 m/s, S. Find the resultant velocity of the plane with respect to the ground.

Answer: 51m/s, at 11o S of E.

Independence of Vector Quantities

Perpendicular vector quantities are independent of one another.

Independence of Vector Quantites Example: The constant velocities in each of

the two dimensions of the boat & river problem, are independent of each other.

Velocity of Boat in Still Water

Velocity of River

with respect to the ground

Example 5- Boat and RiverA boat has a velocity of 4 m/s, E, in still water. It is in a river of width 150m, that has a water velocity of 3 m/s, N.

a) What is the resultant velocity of the boat relative to the shore.

b) How far downstream did the boat travel?

Answer: a) 5m/s, @ 37o above + x axis (E) b) 113m

CONCLUSION OF CONCLUSION OF Chapter 6 - AccelerationChapter 6 - Acceleration