Download Lecture 04 - WebPhysics

Goal: To understand velocity
Objectives:
1) To understand the difference between Speed vs.
velocity
2) To understand the difference between
instantaneous velocity and average velocity
3) To understand relative velocity
4) To understand how to use velocities in multiple
dimensions to solve problems
Run away speeder!
• A speeder who refuses to pull away.
• A lone cop needs to communicate with the
rest of his team to catch this guy.
• If the cop says the speeder is on Highway
70 just past exit 25 going at a speed of
100 miles per hour, does this help much?
Why or why not?
Wrong way!
• The cop has not told anywhere in which
direction the speeder is going, only where
the speeder is and how fast the speeder is
moving.
• So, we need direction.
• However, once you give a direction you
are no longer using speed!
• You are using velocity!
Velocity
• Velocity is a combination of speed and
direction.
• 100 miles/hour is a speed
• 100 miles/hour South or 100 miles/hour
SW are examples of velocity.
Quick example question
• A car travels north from Portland to Seattle
at a constant rate of 70 miles per hour.
• What is the car’s speed?
• What is the car’s velocity?
• What is the net force on the car during this
time (yes, I am that mean that I would
remind you of a previous lecture)?
Velocity vs speed
• Quick question – I know it is a tough one –
a car travels in a circle with constant
speed. Is the acceleration on the car zero
– that is to say is the velocity constant?
Three different “types” of velocity
• Average velocity
• Instantaneous velocity
• Constant velocity
Average Velocity?
•
•
•
What is that? Well average velocity is:
Average velocity = vector distance traveled / time
Average speed = gross distance traveled / time
•
Keep in mind that Velocity is a vector!
•
•
Your turn:
You drive from Seattle to Portland (which is South by
170 miles) in 4 hours.
You then drive from Portland to Astoria (which is 40
miles North and 60 miles West) in 2 hours.
•
A) What is your average speed?
B) What is your average velocity (keep in vector form)?
Instantaneous Velocity
• This is the velocity you are traveling at some
moment
• A snapshot if you will
• This could include but not be limited to:
starting velocity
final velocity
some velocity in the middle
However, you cannot use the instantaneous
velocity to compute distances or average
accelerations…
Constant Velocity
• Sometimes you will encounter a problem
that has a constant velocity.
• You can treat this as an average velocity
• Quick wake up question, if you have a
constant velocity what is the net force on
the object?
Relative Velocity
• What is your current velocity?
Makes no sense
• Sometimes it makes no sense to compute
your total overall velocity.
• So, you use relative velocity.
• That is your velocity relative to something
else, or something else’s velocity relative
to you.
Example
• You are on a train that is moving forward at a velocity of
20 m/s.
• A peanut vendor (yes this would seem odd to you too)
sells you some peanuts and tosses you the bag of
peanuts.
• The peanut vendor is 6 meters behind you (or a -6 m
distance in the forward direction) and tosses the peanuts
with an initial velocity of 6 meters forward and 4 meters
per second upwards.
• A) How long will it take the peanuts to get to you?
• B) From someone outside the train how far through the
air do the peanuts actually appear to travel?
Using multiple dimensions
• Sometimes you will have to solve a problem in
one dimension before you can solve it in
another.
• One example is a swimmer swimming across a
river (not recommended)
• Suppose the water travels downstream at 2 m/s
carrying the swimmer with it.
• The swimmer pushes himself or herself from one
shore to another.
• The result is that they will have a downstream
motion as well as a motion towards/away from
the shore.
Example
• To be written on the board if time permits.
Another case
• A punter punts a football at a 30 degree angle
• This means that the ball will have some velocity
in the vertical and the horizontal.
• Since those dimensions have different forces we
will end up solving each dimension separately.
• For now though, lets just find the initial velocity
(yes sines and cosines may be involved here):
• A) What is the ball’s initial vertical velocity?
• B) What is the ball’s initial horizontal velocity?
Conclusion
• We have examined velocity in its various
forms.
• We have learned the difference between
speed and velocity as well as how to find
the average speed and average velocity.
• We have learned how to tackle velocities
that are in multiple dimensions