Two branches in physics examine the motion of objects:
Kinematics: describes the motion of objects, without looking at the cause of the motion
(kinematics is the first unit of Physics 20).
Dynamics: relates the motion of objects to the forces which cause them (dynamics is the second unit of Physics 20).
As we work through these two units on kinematics and dynamics (and
“Quantity” is the root word for through the rest of physics) we will discuss two kinds of measurements "quantitative" measurements.
This means you're supposed
to get a number answer. A
scalar: scalars have magnitude (a number value), but no
measurement direction. describes qualities of the data,
Examples: time, mass, distance. Mass is a great example, since it like “the apple is red.” has a number value (like 58 kg), but we don't give it a direction
vector: have magnitude and direction
Examples: velocity, force, displacement. Force has a magnitude (like 37 N) and a direction
(like "pushed to the left").
Displacement & 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 displacement, and the time it took to move that far.
The displacement of an object is always measured from some reference point (which is usually
“zero”, at a location at the start of the motion of the object).
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.”
The most simple formula for calculating the displacement of an object is…
Δd = df - di
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 displacement of an object by taking the final position minus the initial position.
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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.
Notice that the word “determine” has been bolded in the question. This is a
“directing word” telling you what to do in the question.
Δd = df - di = 450 - 300 = 150m
Note: If the example had asked for the displacement, we would have to include a direction (like
“East”) in our answer.
Example 2: You start walking home from school. After walking 1.3 km North, you get a phone call on your cell from your mom asking if you can meet her at the mall. You will have to turn around and walk
2.5 km South. Determine your distance and displacement to get to the mall.
Let's start by looking at a quick sketch of the situation, as shown at right.
● From the school you first walked 1.3 km [N].
1.3 km [N]
● You then turned around and walked 2.5 km [S].
If we want the distance you walked, we need to look at all the walking you did, without considering direction. d = 1.3 + 2.5 = 3.8 km
2.5 km [S]
When we look at your displacement, we need to consider the direction that you walked. Even though you walked North at first, turning around and walking South canceled out all of your initial movement. When we measure displacement we are only where you Illustration 1: Walking started and where you finished, not all the stuff in between. We will around after school. consider moving North to be positive, and South to be negative.
d=1.3 km−2.5=−1.2 km = 1.2 km [South]
Notice that the displacement is smaller (and negative, meaning South) when compared to your distance. That's because even though you actually