Download Speed and Acceleration

Newton’s Second Law,
Speed, Acceleration and Energy
Measuring Motion
Measuring Distance

Meter – international (SI) base unit
for measuring distance.
1 mm
= 50 m
Calculating Speed

Speed (S) = distance traveled (d) /
the amount of time it took (t).
S = d/t
Units for speed

Units for speed are relative, and
really any unit that makes sense for
the scale being measured is fine.
However, it will always be a
distance unit / a time unit





Cars: m/h (or mph), km/h (or kph)
Jets: m/h (or mph), km/h (or kph)
Snails: cm/s (why not km/h?)
Falling objects: m/s
Trains: How about mm/h ? (Nope!)
Calculating speed




S = d/t
If I travel 100 kilometer in one hour
then I have a speed of…
100 km/h
If I travel 1 meter in 1 second then
I have a speed of….
1 m/s
Average speed

Speed is usually NOT CONSTANT



Ex. Cars stop and go regularly
Runners go slower uphill than downhill
Average speed = total distance
traveled/total time it took.
Calculating Average Speed


It took me 1 hour to go 40 km on the
interstate. Then it took me 2 more hours
to go 20 km using the surface streets.
Total Distance:


Total Time:


40 km + 20 km = 60 km
1 h + 2 h = 3 hr
Ave. Speed:

total d/total t = 60 km/3 h = 20 km/h
Total _ Dist.
Ave. _ Speed 
Total _ time
Question



I travelled 25 km in 10 minutes. How fast
am I going in m/s?
25,000 meters in 600 seconds
41.7 m/s
Question

I ran 1000 m in 3 minutes. Then
ran another 1000 m uphill in 7
minutes. What is my average
speed?
A) 100
m/min
TotalDist.
= 1000
m + 1000 m = 2000 m
 B) 2000 m/min
TotalTime
3 min + 7 min = 10 min
C) 10=m/min
 D) 200 m/min
Ave speed = total dist/total time =
 E) 20 m/min
2000m/10 min = 200 m/min = D
Velocity

Velocity – the SPEED and
DIRECTION of an object.

Example:
An airplane moving North at 500 mph
 A missile moving towards you at 200 m/s

Question


What is the difference between
speed and velocity?
Speed is just distance/time. Velocity
includes direction as well.
Graphing Speed:
Distance vs. Time Graphs
Denver
Phoenix
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise=?
600 km
3h
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise=?
600 km
3h
Rise/
Distance (km)
Different Slopes
8
7
6
5
4
3
2
1
0
Slope = Rise/Run
= 1 km/1 hr
= 1 km/hr
Slope = Rise/Run
= 0 km/1 hr
= 0 km/hr
Rise = 2 km
Rise = 0 km
Run = 1 hr
Run = 1 hr
Slope = Rise/Run
= 2 km/1 hr
= 2 km/hr
Rise = 1 km
Run = 1 hr
1
2
3
4
Time (hr)
5
6
7
Question
Below=isTotal
a distance
vs. time
graph
ofkm/6 hr
Average Speed
distance/Total
time
= 12
my position =during
a race. What was
2 km/hr
my AVERAGE speed for the entire race?
14
Distance (km)
12
10
8
Rise = 12 km
6
4
2
0
0
1
2
3
Time
Run
= (hr)
6 hr
4
5
6
Question


What does the slope of a distance
vs. time graph show you about the
motion of an object?
It tells you the SPEED
Question

Below is a distance vs. time graph for 3
runners. Who is the fastest?
7
Distance (mi.)
6
5
Bob
Jane
Leroy
4
3
2
1
0
0
1
2
3
4
5
6
35
Time (h)
Leroy is the fastest. He completed the race in 3 hours
Acceleration


Acceleration = commonly thought
of as “speeding up”
Acceleration – the rate at which
velocity changes

Can be an:
Increase in speed
 Decrease in speed
 Change in direction

Types of acceleration

Increasing speed


Decreasing speed


Example: Car speeds up at green light
screeeeech
Example: Car slows down at stop light
Changing Direction

Example: Car takes turn (can be at
constant speed)
Question


How can a car be accelerating if its
speed is a constant 65 km/h?
If it is changing directions it is
accelerating
Calculating Acceleration

If an object is moving in a straight line
Final _ speed  Initial _ Speed
Accelerati on 
Time

Units of acceleration:

m/s2
Calculating Acceleration
Final _ Speed  Initial _ Speed
Accelerati on 
Time
16m / s  0m / s

4s
 4m / s 2
0s
0 m/s
1s
4 m/s
2s
8 m/s
3s
12 m/s
4s
16 m/s
Question

A skydiver accelerates from 20 m/s to 40
m/s in 2 seconds. What is the skydiver’s
average acceleration?
Final _ speed  Initial _ speed
Accel 
Time
40m / s  20m / s 20m / s


2s
2s
2
 10m / s
Newton’s Second Law of
Motion
Answers the question, “How fast will
objects accelerate, relative to their
mass and the force applied to them?”
Acceleration

An unbalanced force causes
something to accelerate.
Acceleration


Acceleration of an object is directly
related to the size of the
unbalanced force and the direction
of the force.
It will accelerate in the direction you
push or pull it.
In general….
Small Force
=
Small Acceleration
F
a
So….if you push twice as hard, it accelerates twice as
much.
In general….
Large Force
F
=
Large Acceleration
a
But there is a twist….


Acceleration is INVERSELY related to the mass
of the object.
Force = Mass X Acceleration
-orF=ma
…where F is the force, m is the mass, and a is
the acceleration. The units are Newtons (N) for
force, kilograms (kg) for mass, and meters per
second squared (m/s2) for acceleration. The
other forms of the equation can be used to
solve for mass or acceleration.
m=F/a
and
a=F/m
In other words…..using the same
amount of force….
F
Small acceleration
Large
Mass
a
Large acceleration
F
Small Mass
a
Newton’s Second Law

Newton, observed those “rules” of
acceleration and came up with his
Second Law of Motion. It is both a
formula and a scientific “law.”
Newton’s Second Law
The acceleration of an object is directly
proportional to the net force &
inversely proportional to it’s mass.
Thus:
 F = ma
 Force = Mass x Acceleration

Newton’s Second Law
Example:
 Engineers at the Johnson Space Center
must determine the net force needed for
a rocket to achieve an acceleration of 70
m/s2. If the mass of the rocket is 45,000
kg, how much net force must the rocket
develop?
 Using Newton's second law, F=ma
 F=(45,000 kg)(70 m/s2) = 3,150,000 kg
m/s2 OR F=3,150,000 N
 Note that the units kg m/s2 and newtons
are equivalent; that is, 1 kg m/s2 = 1 N
Kinetic Energy


If an object is moving, it has
energy. (Be careful, the converse
of this statement is not always
true!)
This energy is called kinetic
energy - the energy of motion.
Kinetic Energy


An object’s kinetic energy
depends on:
the object’s mass.


Kinetic energy is directly
proportional to mass.
the object’s speed.

Kinetic energy is directly
proportional to the
object’s speed.
square of the
Kinetic Energy

In symbols:
1
2
KE = mv
2
Kinetic Energy
 Kinetic
energy is a scalar
quantity. (Scalars are quantities that
are fully described by a magnitude, or
numerical value alone; not a vector.)
 Common
units of kinetic
energy: Joules
 An
object with mass of 1 kg,
moving at 1 m/s, has a kinetic
energy of 0.5 Joule.
Kinetic Energy

Determine the
kinetic energy of
a 625-kg roller
coaster car that
is moving with a
speed of 18.3
m/s.




KE = 0.5*m*v2
KE = (0.5) * (625 kg) *
(18.3 m/s)2
KE = 1.05 x105 Joules
Or 104,653 Joules
Potential Energy


Sometimes work is not converted
directly into kinetic energy. Instead
it is “stored”, or “hidden”.
Potential energy is stored
energy or stored work.
Potential Energy

Potential energy is energy that an
object (system) has due to its
position or arrangement.