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 velocityfinal velocitysome 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