Continue on Warm Up page…
9/9 Convert the following:
6. 3 days to seconds
7. 10,095 m/sec to miles/sec
8. 57 km/hr to m/sec
The Equations…
So how do we know an object is moving?
An object is in motion if its position changes.
The mathematical description of motion is kinematics.
The simplest kind of motion an object can experience
is uniform motion in a straight line or linear motion.
As the car moves, it often undergoes changes in
speed. For example, during an average trip to school,
there are many changes in speed. Rather than the
speedometer maintaining a steady reading, the needle
constantly moves up and down to reflect the stopping
and starting and the accelerating and decelerating.
What is the difference between distance and displacement?
Distance: How far something travels (scalar quantity)
Displacement: How far something travels in a given
direction, the straight line distance from my start
point to end point (vector quantity)
DISTANCE
What is the distance of the biker?
What is the displacement of the biker?
A skier travels from A to B then to C then to D.
What distance does she travel? 420 m
What is her displacement at D?
140 m right of A
SCALAR vs VECTOR Quantities
Scalars are quantities which are fully described by a
magnitude (measurement) alone.
Ex. Distance, speed, and time
Vectors are quantities which are fully described by
both a magnitude (measurement) and a direction.
Ex. Displacement and velocity
If she jogs from A to B to C
Distance traveled = AC + CB + BC = 400 m.
Displacement = 200 m right of A
Scalar vs. Vector
Quantity
Scalar or Vector
10 m/s East
Vector
10 N to the right
Vector
Scalar
35 mi/hr
13 sec.
67 yds North
25 meters
Scalar
Vector
Scalar
Frame of reference
• Based on your perception…describing
something that is moving and comparing it
to something stationary
– Independent and dependent variable
relationship
– What is frame of reference dependent on?
AVERAGE SPEED (scalar)
If an object takes a time interval t to travel a
distance d, then the average speed of the object is
given by:
dist
s
t
PROBLEM SOLVING GUIDELINES
• Make a list of given quantities (Data)
• Convert units if needed
• Make a sketch if necessary
• Identify what is to be determined
• Always solve the equation for the unknown
• Be consistent with units
• Check that the answer seems reasonable
• Physics problems take practice –
the more you do the easier it will be!
Example 1: A runner makes one lap around a 200 m track
in a time of 25 s. What is the runner's average speed?
Givens:
d = 200 m
t = 25 s
Unknown: S
Diagrams:
Duncan Phillips AMCHS ‘07
‘O6 State Gold Medal 1600 m
Base formula/rule:
S= d
Answer:
8 m/s
t
Work:
S= d
t
200 m

25 s
= 8 m/s
Example 2: According to the World Disk Federation, on
April 8,2000, Jennifer Griffin threw a Frisbee for a
distance of 138.56 m to capture the woman’s record.
If the Frisbee was thrown horizontally with a speed of
13.0 m/s, how long did the Frisbee remain aloft?
Givens:
S = 13.0 m/s
d = 138.56 m
t = ?
Diagrams:
Base formula/rule:
S= d
t
Work:
t= d
S
Answer:
= 10.7 s
= 138.56 m = 10.658
13.0 m/s
Example 3: A snail can move approximately 0.30 meters
per minute. How many meters can the snail cover in 15
minutes?
Givens:
S = 0.30 m/min
t = 15 min
d = ?
Diagrams:
Base formula/rule:
S= d
t
Work:
d = st
Answer:
= 50 m
=(15 min) (0.30m/min)
= 50
AVERAGE VELOCITY (vector)
Average velocity is the displacement divided by the
amount of time it took to undergo that displacement.
The difference between average speed and average
velocity is that average speed relates to the distance
traveled while average velocity relates to the
displacement.
x=xf-xi (found by finding the
V = displacement =
elapsed time
v
x
t
x
t
difference)
-xf means final (you may also
see Xf)
-xi means initial (you may also
see Xi)
-Need to have an
origin/reference point
Example 1: A vehicle travels 2345m in 315 sec toward the
evening sun. What was its velocity?
Example 2: What is a vehicles displacement if it is
traveling 120 km/hr north for 30 min?
Example 3: Houston is 200km away, how long will it take a
southbound bicyclist traveling at 100 m/s?
Observe the animation of the three cars below. How
would you describe the motion of the red car?
the green car?
the blue car?
The rate at which velocity changes is ACCELERATION
ACCELERATION
Acceleration is the rate of change of velocity. The change
in velocity ΔV is the final velocity Vf minus the initial
velocity Vi.
Units: m/s2
A positive acceleration means an increase in velocity; a
negative acceleration usually means a decrease in
velocity (deceleration).
Note that negative acceleration
is in OPPOSITE direction of the
velocity
Example 3: An object starts from rest with a constant
acceleration of 8 m/s2 along a straight line.
Find the speed at the end of 5 s
Givens:
Vo = 0 m/s
a = 8 m/s2
t = 5 s
Vf = ?
Diagrams:
Answer:
Vf = 40 m/s
Work:
v f  vo  at
Vf = 0m/s + (8m/s2)(5s)
Vf = 40 m/s
Example 4: A truck's speed increases uniformly from
15 km/h to 60 km/h in 20 s. Determine the acceleration.
Givens:
vo = 15 km/h
= 4.17 m/s
vf = 60 km/h
= 16.7 m/s
t = 20 s
a = ?
Diagrams:
Answer:
= 0.63 m/s2
Work:
a
v f  vo
t
16.7  4.17m/s

s
20
= 0.6265 m/s2
Example 5: A bus moving at a speed of 20 m/s begins to
slow at a constant rate of 3.0 m/s2. How long before it
stops?
Givens:
Vo = 20 m/s
Vf = 0 m/s
t =?
a = - 3 m/s/s
Diagrams:
Answer:
t = 6.67 s
Work:
t = Vf – Vo
a
t = 0 – 20 m/s
-3 m/s2
t = 6.6667 s