Honors Physics - Chapter 2: Lesson 2

Chapter 2: Lesson 2

Velocity and Vectors

Chapter 2: Lesson 2 - Velocity and Vectors

Equations:

An important piece of paper to have handy when studying physics is your equation sheet. You never have to memorize any of the equations in class. You just have to know how to use them, manulipate them to solve for the unknown, and what each abbreviation stands for. A copy of the equation sheet is under resource materials on this website and on google classroom. It can also be found HERE. It is helpful to have a copy handy so you can mark equations on the sheet when we talk about them.

Before we talk about speed, we first need to know what a rate is. A rate is a quantity divided by time. If you look at your equation sheet, any equation that is divided by time is a rate. We will be coming back to this term many times this year!

Speed:

Speed is the measure of how fast something is moving. Speed is the distance covered per unit of time.

Instantaneous speed is the speed at any given instant. This is one of those times where the vocabulary word actually matches what it means! When you look down at your speedometer in your car, you are looking at the instantaneous speed. It is how fast you are moving at the instant that you looked.

When you are talking about the speed over a period of time, you are actually calculating the average speed.

The equation for average speed.

Check Your Understanding:

On the two questions below, think about the question, then click on the down arrow when you have your answer to check to see if you are correct. Use the animation to answer the two questions.

What is the speed of the car when it is stopped?

It is at rest, so 0 m/s.

2. What is the average speed of the car?

The average speed of the car is the total distance it traveled (5 miles) divided by the total time it took to get there (.2 hours.) The average speed is 5 miles / .2 hours = 25 miles/hour

Velocity:

There is a BIG difference between speed and velocity. Actually, that BIG difference is just one word, direction. Speed does not have a direction, it only tells us the magnitude. Magnitude is a fancy word for size. Magnitude tells us how much there is of something. Speed just tells us how fast, not the direction the obejct is moving in.

Velocity, is the speed in any given direction. Velocity has both direction and magnitude.

If an object has a constant velocity, it has to have BOTH a constant speed and a constant direction. If EITHER the speed or direction is changing, then you have a changing velocity. Only one has to change for the velocity to change.

We will abbreviate BOTH speed and velocity with a lowercase v. The unit for speed and velocity is meters per second (m/s).

The equation for velocity. This is the equation that is on your equation sheet and the one that we will be using. Velocity equals distance divided by time.

The unit for velocity is m/s. That comes right from the equation, v=d/t.

Meters (m) is the unit for distance and seconds (s) is the unit for time.

Scalar and Vector Quantities:

We already learned that magnitude was a fancy word for size. A scalar quantity is a quantity that has magnitude only. An example of a scalar quantity would be speed. It only tells us how fast something is going, the magnitude.

A vector quantity is a quantity that requires both magnitude and direction. An example of a vector quantity would be velocity.

Vectors are represented by arrows. An arrow can tell us where an object started and in what direction it is going. The arrow above represents a vector. The tail of the vector tells us where the object started from, and the head of the vector tells us what direction it is moving in.

Distances, velocities, and forces can all be represented by vectors. The magnitude of the vector is represented by the length of the arrow. Look at the picture above. The vector that represents the velocity 100 m/s is twice as long as the vector that represents the velocity 50 m/s.

Have you watched Despicable Me?

If YES, then you should remember a villian named vector.

If NO, then you should watch it. It's a good movie.

Either way... watch the short video clip to see how vector commits his crimes.

Adding and Subtracting Vectors

A vector that respresents the sum of the other two vectors is called the resultant. The resultant always points from the tail of the frst vector to the tip of the last vector. It is the RESULT of when we add or subtract two vectors together.

You can add vectors together when the arrows are pointing in the same direction. In the picture above, you walk from your house to the store, which is 5 m. Then, you walk from the store to your Aunt's house, which is 2 m away. How far did you walk from your house to your Aunt's house? That is easy, you just have to add 5 m + 2 m to get 7 m.

You can subtract vectors when they are pointing in the opposite direction.

Check Your Understanding:

On the two questions below, think about the question, then click on the down arrow when you have your answer to check to see if you are correct.

Let's say there is an airplane that is flying with the wind at its tail. (The wind is pushing at the back of the airplane.) The airplane's velocity is 100 m/s and the wind's velocity is 10 m/s. What is the resultant velocity of the airplane?

10 m/s + 100 m/s = 110 m/s

2. Now, let's say there is an airplane that is flying with the wind at its head. (The wind is pushing at the front of the airplane.) The airplane's velocity is 100 m/s and the wind's velocity is 10 m/s. What is the resultant velocity of the airplane?

100 m/s - 10 m/s = 90 m/s

You have finished Lesson 2!

Be sure to head over to google classroom and fill out the exit pass.

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