# Definitions

Two branches in physics examine the motion of objects:

- Kinematics: describes the motion of objects, without looking at the
*cause*of the motion (this is what we will be focusing on now) - Dynamics: relates the motion of objects to the forces which
*cause*them (dynamics pops up later on in Physics 20).

**Quantity**" is the root word for "

**quantitative**" measurements. This means you're supposed to get a number answer. A

**qualitative**measurement describes

**qualities**of the data.

In kinematics and dynamics we will discuss two kinds of measurements (quantities):

- scalar: scalars have
**magnitude**(a number value), but**no direction**

*e.g. time, mass, distance. Mass is a great example, since it has a number value (like 58 kg), but we don't give it a direction (like "down").* - vector: have
**magnitude**and**direction**

*e.g. velocity, force, displacement. Force has a number value (like 37 N) and a direction (like "pushed to the left").*

# Position & Time

In kinematics we need to be able to have a way to describe the motion of the objects we will be studying, whether it's a car or an atom.

The most basic information you must have to describe the motion of an object is its position and the time it was at that position.

- The position of an object is always taken from some
**reference point**(which is usually "zero" on the scale).- Although we use the words "
**distance**" and "**displacement**" interchangeably in everyday language, they mean very different things in physics. - The distance between two objects is
**scalar**, since it doesn't matter which direction you measure it from.*e.g. "We are standing 2.3m apart."* - The displacement of an object is a
**vector**, since you have to state the direction the object has traveled.*e.g. "The car moved 2.56km east."*

- Although we use the words "

The most simple formula for calculating the change in an object's position is…

Δd = d_{f} - d_{i}

- The Δ symbol is the greek letter "
**delta**" and means "a change in…" - The subscript "
**f**" and "**i**" stand for**final**and**initial**. - So, in this formula, we calculate the change in position of an object by taking the final position minus the initial position.

**determine**" has been bolded in the question. This is a "

**" telling you what to do in the question. Get used to seeing these, since they are used on the Physics 30 diploma.**

*directing word*Example 1: A truck is passing a mark on the road that says 300m, and then passes another one 10s later that says 450m. **Determine** the distance the truck moved.

Δd = d

_{f}- d_{i}= 450 - 300 =150m

Note: If the example had asked for the displacement, we would have to include a direction (like "east") in our answer.

# Average Velocity

This leads to the first major formula for the calculation of "average velocity".

v = velocity (m/s)

Δd = displacement (m)

Δt = time (s)

- It is called "
*average*velocity" because it does not take into consideration all the slowing down or speeding up during the object's movement. - Instead, all you consider is the
**total**displacement divided by the**total**time. - When you write the formula, you can skip putting in the delta symbols, and the arrows (they're just there to remind you that those are vectors).

Example 2: I try to run the 100m race to break the world's record! Unfortunately, it takes me 16.83s to complete the run. **Determine** my average velocity.

v = d / t

= 100m / 16.83s

v = 5.94m/s

- This is my
**average**velocity. It does not take into account that I have to speed up at the start of the race, or maybe slow down near the end. - Most of the time we talk about velocity in kilometres per hour (km/h).
- To convert
**m/s**to**km/h multiply**by**3.6**(which is an exact value and has an infinite number of sig digs.) - The answer from above is 21.4km/h.
- If you ever do a calculation like this, use the original number on your calculator, not the rounded off answer that you first wrote down.

- To convert

Note that in the above example, the displacement and the velocity were positive numbers.

- Positive and negative tell you which direction you are going with respect to the reference point. (Remember, these are vectors.)
- A positive velocity means you are moving forward , to the right, or up, while negative means you are going backwards, to the left, or down.
- This is why it is so important not to confuse d
_{f}and d_{i}

Example 3: A high speed train might be built between Edmonton and Calgary. It could travel between the two cities at an average velocity of +227km/h. The trip would take 1.2h. **Determine** how far apart Edmonton and Calgary are.

- Since I have a velocity and time that will cancel out nicely, I'll get an answer in kilometres.
- If you're uncertain, you should
**always**change everything into standard units.

v = d / t

d = vt

= (227km/h) (1.2h)

= 272.4km =

2.7e2 km

# Uniform Motion

If the velocity of an object is the same throughout the entire time, it has a **constant** (AKA **uniform**) velocity.

- You still use the same formula as for average velocity.
- Uniform motion is the easiest kind of motion to describe and measure, since it is always the same.
- In the examples you've done so far, and in most questions you'll do for now, you assume that it is uniform motion.

# Instantaneous Velocity

But what about when you are calculating the velocity of an object traveling *without* uniform velocity?

- This is what would be the situation if you ask your friend how fast she is driving when you're in a car.
- She'll glance down at the speedometer and tell you how fast she is going, but that is only how fast she was going at that instant of time!
- A split second later, she might be going a bit faster or a bit slower. Most people don't drive their cars at a totally constant velocity.
- That's why we call the measurement she gave you an instantaneous velocity.

# Velocity vs Speed

One last note for you. Avoid using the word "speed" when describing any velocity.

- Speed is a scalar quantity (it doesn't have direction).
- We usually want the velocity of an object.

"What speed did you drive today along Yellowhead?" -> "I drove at 72km/h."

"What was your velocity along Yellowhead?" -> "My velocity was 72km/h East."