Goal: To understand linear motions

Objectives:1) To understand the difference between

Speed vs. velocity2) To understand Acceleration

3) To understand the relationships between Distance and velocity

4) To understand the relation ships between Velocity and acceleration

5) To understand the relationships between Distance and acceleration

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.

• In this class we will mostly deal with velocities in 1 dimension, that is 1 direction, although if you have 2 dimensions, you break the velocities into each dimension.

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 last week’s lecture)?

Acceleration

• What do you think of when you hear the word acceleration?

Acceleration is:

• The rate at which your velocity changes.

• Note this changes velocity – what does that tell you about acceleration?

• 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?

Now that we know what everything means, how do we use it?

• First lets compare distance and velocity.• Lets see if you know how to do this

already…• Person A travels at a constant velocity of

50 miles per hour west for 4 hours.• Person B travels at an average velocity of

50 miles per hour west for 4 hours.• How far do persons A and B travel (yes

distance has direction also)?

Two ways to do this!

• 1) Unit conversion, if 1 hour = 50 miles (i.e. 50 miles per hour) you can convert hours to miles.

• 2) Distance = average velocity * time

Average Velocity?

• What is that?• Well average velocity is:• Average velocity = distance traveled / time

• Okay lets do an example of this.• A car travels north from Portland to Seattle.• The car hits traffic along the way as well as

having different speed limits in different areas.

• If Seattle is 160 miles north of Portland and the trip takes 4 hours then what is the average velocity of the car?

Changing velocity

• If you change your velocity (even it if it just changing the direction) that is an acceleration.

• However, how do we find the new velocity.

• How do we find the acceleration.

• First acceleration:

• Acceleration = change in velocity / time

Questions from book:

• What is the acceleration of a car that zooms by you at a constant speed of 100 miles per hour?

• Which has a greater acceleration – a jet that goes from 1000 km/h to 1010 km/h in 10 seconds or a skateboarder who goes from 1 km/h to 3 km/h in 1 second?

Velocity after acceleration

• Acceleration changes velocity.• New velocity = Old velocity + acceleration * time• Or, change in velocity = acceleration * time• Sometimes the new velocity is bigger,

sometimes it is smaller.

• Lets do some examples.• A truck is coasting down a hill. Will its

acceleration be positive or negative?

Run away truck!

• A truck looses its breaks and accelerates down a hill at an acceleration of 2 m/s2

• The trucks initial velocity was 30 m/s.• What will the truck’s velocity be after 10

seconds?

• To save himself the truck driver pulls onto a run away truck road – which is a common road on a mountain road.

• Will the acceleration on the truck be negative or positive?

Save the truck!

• Imagine that the truck starts at 50 m/s and the acceleration on this road in the is -5 m/s2

• What will the trucks velocity be after 2 seconds?

• How long will it take for the truck to stop (I know, this one is tougher, but think about it)?

Distance vs. acceleration

• For this course when we compare these two it will be using an object that is either starting at rest or ending at rest.

• The distance that an object will move – assuming constant acceleration – will be:

• Distance = ½ * acceleration * time * time

• Challenge question: How would this distance change if the object was initially moving?

Examples

• For the run away truck, lets imagine it started at rest and accelerated at a rate of 2 m/s2 up to a velocity of 50 m/s (down the hill).

• 1) How long will it take the truck to get to 50 m/s?

• 2) How far will the truck move in this time?

Deceleration example

• This is done almost the same as acceleration for distance, but you reverse the velocity.

• If the truck decelerates at 4 m/s2 then how long does it take the truck to stop?

• How far does the truck move in this time?

10 minute intermission

• In the next hour our goal will be to understand how gravity works on the surface of the earth.

• Objectives:• 1) to understand gravitational acceleration• 2) to learn about gravities effects on upward

motion• 3) to explore gravities effects on downward

motion

Gravity

• It pulls downward on the surface of the earth.

• The acceleration is nearly constant – and for this class we will take it as a constant.

• The true value for most of the earth is 9.8 m/s2, but you are welcome to use 10 m/s2 in this course.

• Opps, I made a mistake – what is my mistake?

What does that mean?

• That means every second, you velocity changes by 10 m/s in the downwards direction.

Gravity up?

• What is the value of gravity in the upwards direction?

• What is the value for gravity in the sideways direction?

Example

• You toss a ball straight up into the air at an initial velocity of 50 m/s.

• How fast will the ball be moving after 1 second?

• How long will it take for the ball to stop?

Back down…

• Lets compare its downward motion to the upward one.

• 1 second after the ball stops, what will the velocity of the ball be?

• How does this velocity compare to the velocity 1 second before the ball stopped?

Using that fact

• What will the velocity of the ball be when it comes back to you?

• How long did the ball fall for?

• How far did the ball go (hint, find the distance it travels in the time it takes to fall back down)?

• What was the ball’s total hang time?

A ball falls off of a cliff!

• If the ball falls for 5 seconds how far will it fall?

• What will the ball’s velocity be just before it hits the ground if it hits the ground at that point?

Challenge!

• You drop a ball of the Sears Tower (lets say height here is 500 m).

• How long will it take for the ball to hit the ground (warning this one takes a little bit of algebra)?

Since we have some extra time:

• Lets do a projectile question and put everything together.

• A punter punts a football at a 45 degree angle (this means that the velocity it goes up will be the same as the velocity it goes down the field).

• If the kicker kicks the ball and it goes up at a velocity of 15 m/s then:

• How long will the ball be in the air (hint, find how long it takes for the ball to stop)?

• How far will the ball travel down the field (hint, you have the time and velocity)?

Conclusion

• We have learned most of what there is to know about linear motion.

• We have learned how to use distances, velocities, and accelerations to find other values – and how to find time.

• The only way to make this harder is to add in a 2nd dimension.