Speed

Velocity

Acceleration

A scalar is a quantity which has the magnitude only (mass, length, time,

volume, temperature).

A vector is a quantity which has both the magnitude and direction (velocity,

force).

In physics we use System International (SI) units.

2

In physics we need vectors because the real world is three dimensional.

System International or the metric system is used in all countries aside from

the USA; here the British System is in use.

1. Length: the meter (m) [1 ft = 0.305 m, 1 inch = 2.54 cm= 2.54!10-2 m]

2. Mass: the kilogram (kg) [1 slug = 14.9 kg]

3. Time: the second (s) [the same as in British System]

Mechanics and Forces

3

1. Time (second " s)

2. Distance (meter " m )

3. Speed (m/s)

4. Velocity (speed and direction)

9. Torque (N·m)

5. Acceleration (m/s2)

6. Force (newton " N)

10. Linear momentum (kg·m/s)

7. Kinetic, potential energy, and work (joule " J)

8. Power (watt " W)

12. Frequency (hertz " Hz)

11. Angular momentum (kg·m2/s)

Motion with Constant Velocity and Constant Acceleration

Constant velocity:

- Equal distance covered in equal time intervals:

4

Question: How we can describe motion with

constant velocity and acceleration?

Constant acceleration:

- Equal increments of speed gained in equal time intervals;

- Distance increases in each time interval.

Horizontal Motion at Straight Line

5

# We want to understand how objects are moving, so we will:

- discuss various types of motion;

- calculate parameters of motion.

# For motion we will use the following quantities:

Distance, time, speed, velocity, and acceleration.

Using the total distance and the total time we can find the average speed.

We also can find the average speed using change in distance and change in time.

Total distance (dtotal ) = dfinal - dinitialTotal time (ttotal ) =

= tfinal - tinitial

initialinitialdt , finalfinal dt ,

6

Average and Instantaneous Speed

t

d

tt

ddv

initialfinal

initialfinal

av!

!=

"

"=

timetotal

distance total speed average =

interval short timevery

distancein change speed ousinstantane =

shortvery

instt

dv

!

!=

The unit of speed in the System International: m/s

Average speed, vav

Instantaneous speed, vinst

in time change

distancein change speed average =

total

total

av

t

dv =

av

total

total

v

dt =

totalavtotaltvd =

7

A car was traveled during 1 and 3 hours.

hkmvhkmv

htht

/40,/60

3,1

21

21

==

==

Find the average speed.

total

total

av

t

dv =

kmhhkmtvd 60)1)(/60(111 ===

hkmvav

/45=

Average Speed

1. Equation used:

3. Answer:2. Solution:

hkmh

km

t

dv

total

total

av/45

4

180===

hhhttotal

431 =+=

kmkmkmdddtotal

1801206021

=+=+=

kmhhkmtvd 120)3)(/40(222 ===

Speed and Velocity

8

# Speed is just a positive number (speed is a scalar).

# Velocity has the magnitude (a number) and the direction (velocity is

a vector).

# For speed we need to know only the number.

# For velocity we need to know both the magnitude and direction.

Speed

Velocity

If an object is moving, we

can use quantities “speed”

and “velocity”.

The speedometer of the truck #1 moving to the east reads 90 km/h. It passesanother truck, # 2, that moves to the west at 90 km/h.

1) Do both trucks have the same speed?

2) Do they have the same velocity?

3) What speed we are reading on the speedometer:

average or instantaneous?

Speed and Velocity

Yes No

Yes No

# 1

# 2

9

Instantaneous

Average

Motion with Constant Speed: Graphs

10

t

v1) Speed vs. time

It’s important to understand how we can show a motion using graphical method.

initialt

t!

d!

finalt t

initiald

finald

d 2) Distance vs. time

constvt

d==

!

!=

in time change

distancein change

t

dv =

Speed = const

Speed = const

0

vtd =v

dt =

DistanceSpeed Time

t

v

tt

vva

initialfinal

initialfinal

av!

!=

"

"=

11

in time change

yin velocit change on accelerati =

The unit of acceleration in the System International: m/s2

Acceleration shows how fast an object changes its velocity.

Acceleration

Acceleration during motion along straight line:

If an object is moving with constant velocity, acceleration is equal zero:

00

=!

="

"=

ttt

vva

initialfinal

initialfinal

av

12

v

v!

t! t

t

v

tt

vva

initialfinal

initialfinal

av!

!=

"

"=

Positive and Negative Acceleration

Positive acceleration: velocity increases with the time.

Negative acceleration: velocity decreases with the time.

v

v!

t! t

t

v

tt

vva

initialfinal

initialfinal

av!

!"=

"

"=

finalfinal tv ,

initialinitialtv ,

initialinitialtv ,

finalfinal tv ,

13

Equations for Horizontal Motion at Straight Line

Acceleration is constant, velocity is changing:

Acceleration is zero, velocity is constant:

vtd = time-velocity,- distance, tvd !

2

2at

tvdinitial

+=

2

finalinitial

av

vvv

+=

2

2at

d =

Average velocity (speed):

Distance (accelerate from the rest):

Velocity (speed) after time t: atv =

Distance (accelerate while moving at

constant speed):

v

dt =

t

dv =

Motion at Constant Acceleration: Graphs

14

d

t

a

t

v

t

atv =

consta =2

2at

d =

1) Acceleration

2) Speed

3) Distance

Find the distance traveled by the car

for 4 s if it started to move from the

rest at the acceleration of 3 m/s2.

2

2at

d = mssm

242

)4)(/3( 22

==

d Distance vs. time

0

1) Car B moves faster

2) Car A moves faster

3) Both cars have the same speed

4) Note enough data

t

Distance vs. Time

15

Graph below shows distance vs. time for moving cars, A and B.

Which answer is correct?

A

Bt

dv =

The slope of the distance vs. time graph is the speed.

vtd =

1t

vSpeed vs. time

0

1) Acceleration of car B is larger

2) Acceleration of car A is larger

3) Both cars have the same acceleration

4) Note enough data

t

Speed vs. Time

16

Graph below shows speed vs. time for two moving cars, A and B.

Which answer is correct?

A

B

t

va =

The slope of the speed vs. time graph is the acceleration.

atv =

1t

A car was traveled at the average speed of 5 m/s for 1 hour. The

distance traveled by the car is:

Speed and Time

1) 0.3 km

2) 3 km

3) 18 km

4) 1.8 km

17

kmmssmvtd 1800018)6060)(/5( ==!==

vtd =

50 kg are equal:

Conversion

1) 5!103 g

2) 5!10-3 g

3) 5!10-4 g

4) 5!104 g

18

ggkg 43105105050 !=!=

ggkg 31010001 ==

19

Relative Velocity

v=8 m/sv=2 m/s

8 m/s 2 m/s=

6 m/s

Sometimes an object has two velocities at the same time. Let’s say a

person is walking on the train at 2 m/s in the opposite direction of the

train’s motion at 8 m/s.

How fast this person is going relative to someone on the ground?

We will use vector’s addition:

EastWest