Transcript Speed and Acceleration Motion

Speed and Acceleration
Motion
Chapter 2
Speed and Acceleration
What is time?
• A particular moment (EX: 3:30 pm) or an interval of time
(EX: the race lasted 30 minutes)
• Measured in hours, minutes, days years
• Scientists measure in seconds
• Must have a number and a unit
Time measurements
• How many seconds are in a minute?
• How many minutes are in an hour?
• How many hours are in a day?
• How many days are in a year?
• How many year are in a century?
What is distance? How far it is from one point to
another
Motion and Position
• Position –location of an object
• A reference point is needed to determine the
position of an object
• Motion occurs when an object changes its
position relative to a reference point. Therefore,
movement is compared to a reference point
• Are you moving now? Compared to what?
• A frame of reference is a coordinate system in
which the position of the object is measured.
Distance
• An important part of describing the motion of
an object is to describe how far it has moved
which is referred to as distance.
• Distance is a measure of how far it is from one
point to another, how far something has
moved.
• Measured in units of length
• English system = inches, feet and miles
• Metric system (SI units)= Millimeters,
centimeters, meters and kilometers
• 1 m = 100 cm: 1 kilometer = 1000m
What SI unit would you use?
• What unit would you use to measure the
distance home?
• What unit would you use to measure your
height?
• What unit would you use to measure your hand
span?
• What unit would you use to measure the width
of your pencil lead?
Displacement
• Displacement is the distance and direction of
an objects change in position from the starting
point.
• Quick Question: How are distance and
displacement different?
Speed
• Speed is the distance an object travels per unit
of time. A measure of how quickly an object
moves from one place to another. It is the
rate at which distance is traveled or rate of
change in position. Objects that are not
moving are said to have a speed of 0 m/s.
• Any change over time is called rate.
• Speed is the rate at which distance is traveled
or the rate of change in position
Calculating Speed
• You need the distance traveled and the time
taken to travel that distance
• Speed (S or V) = distance(d)/time(t)
Units for Speed
• Speed = Meter per sec (m/s), Miles per hour
(mi/hr), inches/second
• Distance = meters (m), kilometer (km), miles
(mi)
• Time = seconds (s), hours (hr)
Speed Triangle
• S = speed
• D = distance
• T = time
Practice Problem: Calculating
Speed
• Formula: Distance traveled divided by the
time taken.
• If you drove 90 miles in 1.5 hours, what is your
speed for the trip?
Solving for other variables:
• How far would you drive if you drove for 2
hours at 60mph?
Problems
1. Nascar driver, Jeff Gordon, has a car that is one of
the fastest on the circuit. If it travels 600 miles in
4 hours, what is his cruising speed?
• v = d/t
• V = 600 mi/4 hrs
• V = 150 mi/hr
2. The fastest car on Earth, a German-made
Thrust SSC, would win every Nascar race in
America. If it takes 0.5 hours (30 minutes) to
travel 380 miles, what is its speed?
• v = d/t
• v = 380 mi/ 0.5 hr
• v = 760 mi/h (mph)
3. The fastest train on Earth, the TGV from
France, can travel at faster speeds than trains
in the United States. During a speed test, the
train traveled 800 miles in 2.5 hours. What is
its speed?
• v = d/t
• v = 800 mi/ 2.5 hr
• v = 320 mi/h (mph)
4. Spirit of Australia, a hydroplane boat, made
speed records by traveling 239 miles in 0.75
• hours (45 minutes). What is its recordbreaking speed?
• v = d/t
• v = 239 mi/ 0.75 hr
• v = 318.67 mi/h (mph)
5. The fastest plane ever made, the Lockhead
SR71, was able to travel 2200 miles per hour.
• Based on this speed, how far could it travel in:
a. 2 hours? b. 3 hours? c. 5 hours?
• v = d/t
• v = 2200 mi/ 1 hr
• v = 2200 mi/h (mph)
6. How much time does it take for a bird flying at
a speed of 45 miles per hour to travel a
distance of 1,800 miles?
• t = d/v
• t = 1800 mi /45 mi/hr
• v = 40 hrs
7. A cheetah runs at 60 mph for a distance of 0.5 miles.
How long does this take? Change answer to seconds.
• t = d/v
• t = 0.5 mi/ 60mph
• t = 0.008 hr
• 0.008 hr x 60 sec = 0.48 secs
1hr
8. A comet is cruising through the solar system
at a speed of 50,000 kilometers per hour for 4
hours time. What is the total distance traveled
by the comet during this time?
• d = vt
• d = 50,000 km/h X 4 hrs
• d = 200,000 km
9. A runner runs 6.9 mph for 54 minutes. What
distance did the runner travel?
• d = vt
• d = 6.9 mph X 54 min
• d = 372.6 mph/min (Does this make sense)
• Must change minutes to hours
• 54 min X 1 hour = 0.9 hr
60 min
• d = 6.9 mph X 0.9 hr = 6.2 miles
Types of Speed
• Constant speed = speed that is not
changing. Usually speed is not
constant!
• Average speed – total distance traveled divided
by the total time of travel, average of all speeds
over time traveled. Example: Distance to San
Antonio, Texas = 1000 miles. Time traveled = 15
hours. What is the average speed?
• Instantaneous speed – speed at a given point in
time
Graphs
Graphing Speed
• Distance - time graph or also called a position - time
graph shows the motion of an object over a period of
time.
• Time is plotted on the horizontal axis of the graph and
distance traveled is plotted along the vertical axis
• Slope of a distance vs time graph or a position vs time
graph will tell us the speed of an object
• Slope = rise (vertical) /run (horizontal)
• Label the Axis
• Distance(position) is dependent variable
• Time is the independent variable
Position vs Time Graph = SPEED
Distance vs Time Graph = Speed
• Shows distance traveled in relation to time traveled
• Shows distance and direction of an object from its starting point.
Needs to be expressed with a number and a direction.
• Line sloping upward – steady speed
• Change in upward slope = changing speed
– Steeper = faster
• Flat line – no motion
Downward slope – returning to start
Speed and Velocity
• We use the letter “V” to represent speed. The
letter “V” stands for velocity
• Velocity = includes the speed and direction of
an object
• Velocity can change even though the speed
may not EX: Escalator in the mall
• Speed – tells you how fast you are going
• Velocity – gives a speed along with a direction
Acceleration Speed and velocity
• Acceleration is rate of change in velocity. When the velocity of
an object occurs, the object is accelerating.
• Remember that velocity includes the speed and direction of an
object. Therefore acceleration occurs when an object changes
its speed, its direction, or BOTH. It is the amount your speed
increases compared to how long it took to increase
• Examples of acceleration: Speeding up, slowing down and
change direction
• Speed increases- positive acceleration (acceleration)
• Speed decreases – negative acceleration (deceleration)
• Example of changing direction: Fairs wheel, carousel, race car
track. Turning a corner.
• Is acceleration occurring in these situations?
Calculating Acceleration
Acceleration = Change in speed/change in time OR
Acceleration = (final velocity – initial velocity) /
time
a = Dv/t
Units for Acceleration
• Acceleration = m/s2 , m/s/s, mi/hr2
• Velocity = m/s, mi/hr
• Time = s, hr
change of velocity
accelerati on 
time interval
• Dv = Vf - Vi
Dv
a
t
• A negative acceleration means that the object
is slowing down.
• EX: -20cm/sec2 means tha the speed is
decreasing – this can also be referred to as
deceleration
• Zero Acceleration – traveling at a constant
speed in one direction
• Free Fall is 9.8m/s2 = accelerates at 9.8m/s for
every second that it falls. This is the force of
gravity pulling down on the object
Calculating Positive Acceleration
• If a jet airliner reaches 80m/s at the end of the
run way in 20s. How much did the airliner
accelerate if it started from rest?
Calculating Negative Acceleration
• If a skateboarder is skating at a speed of 3m/s
and comes to a rest in 2 seconds. Calculate the
acceleration.
Graph
• Speed vs time Graph – shows how speed
changed with time – acceleration is the slope
of the speed –time graph.
Speed Time graph = Acceleration
Speed vs Time Graph = Acceleration
Motion and Force
• A force is a push or a pull. It can cause the motion
of an object to change.
• EX: kicking a soccer ball, Earth’s gravitational pull
on you, force exerted by the floor on your feet
• Forces do not always change velocity. When two
or more forces act on an object at the same time,
the forces combine to form the net force.
• Forces on an object that are equal in size and
opposite in direction are called balanced forces.
Net Forces: Balanced and Unbalanced Forces
• Unbalanced Forces are when two unequal
forces are applied to an object. The object
moves in the direction of the larger force.
• The net force will be the difference between
the two forces because they are in opposite
directions.
• If the object is pushed in the same direction,
the forces are combined. (added together)