Lesson 1 - Describing Motion: Reference Frames and Acceleration
Page 1: Reference Frames
Scenario motivation: Have you ever felt car sick? That happens when what your body feels (like bumps and turns) doesn't match what your eyes see (like a steady book). If you're reading in a moving car, your body feels the car moving, but your eyes see the book and the car's inside as still. This difference can make you feel sick.
Key idea: A 'reference frame' is just a fancy way of saying 'your point of view'. It's what you use to describe how fast something is moving and in what direction. It's like picking a spot to watch from.
Inside the car (your frame): From your spot inside the car, the car seems still, so its speed is 0 \text{ km/h} to you. Things inside the car also look like they're not moving compared to you.
Outside the car (the road's frame): If you were standing on the road, the road, buildings, and trees would look still. The car would look like it's moving forward at a speed (like 90 \text{ km/h}).
Two common points of view in daily life:
Car's point of view: From inside the car, the car's own speed is 0 \text{ km/h}. Everything outside (like the road) seems to rush backward at about the car's speed. For example, the road would seem to move at -90 \text{ km/h} past you.
Road's point of view: From beside the road, the road is still (0 \text{ km/h}). The car looks like it's speeding forward at about +90 \text{ km/h}.
Important concept: Reference frames aren't fixed. You can choose which point of view (frame) to use to talk about motion. But once you pick one, you have to stick with it when describing different things moving.
Why you need to say which frame you're using: How you describe motion depends on your chosen point of view. For example, if you and a friend are facing each other in a classroom, you might describe the same motion differently because you have different reference frames.
Classroom example: When your teacher walks from the front of the room to the back (Figure 3), you and your friend might describe it differently:
From the back of the room: Your friend sees the teacher moving closer, toward them, at about 1 \text{ m/s}.
From the front row: You see the teacher moving away from you (toward the back) at about -1 \text{ m/s}. (The minus sign means moving in the opposite direction from what your friend said).
The teacher isn't moving differently; it's just how each person describes it from their own point of view.
What this means in real life: To share information about where something is or how it's moving, you need to say which reference frame you're using. For example, saying "look at the car to my right" or "look at the car to your left" tells someone your point of view.
Motion looks different in different frames: In the car's frame, bushes outside might look like they're moving backward, while the car mirror is still. In the road's frame, the car is moving forward, and the bushes are still.
Describing reference frames is about perspective: Phrases like "I see Mr. Garcia walking away from me" versus "I see Mr. Garcia walking toward me" show two different points of view or reference frames.
Page 2: Describing Reference Frames
You and a classmate see the same thing (the teacher walking), but you describe it differently because you're using different points of view or frames:
Your friend in the back of the room sees the teacher walking in front of her and toward her: the teacher’s speed and direction (velocity) is forward, about +1 \text{ m/s}.
From the front row, you see the teacher walking away from you and behind you: the teacher’s velocity is backward, about -1 \text{ m/s}.
Core idea: How you describe where something is or how it's moving depends on your point of view. You must say which point of view you are using when describing how something moves.
Everyday clues for frames: When you're talking to someone, phrases like "look at the car to my right" or "to your left" tell them which point of view you're using to describe where the car is.
Motion depends on the frame: A simple scene (bushes, a car, a mirror) can look like different motions depending on your viewpoint.
Takeaway: Always state your reference frame (your point of view) when talking about motion so everyone understands what you mean.
Page 3: Acceleration
Think about car ads that say a car goes "from 0 to 60" really fast. That's talking about 'acceleration'. Acceleration is how quickly an object's velocity (speed and direction) changes.
Key definition: Acceleration is how fast an object's velocity (its speed and direction) changes over time.
Remember, velocity includes both how fast something is going (speed) and where it's headed (direction). So, if either the speed or the direction (or both) changes, that's called acceleration.
Three ways an object can accelerate:
Speeding up (positive acceleration): The object goes faster over time.
Slowing down (negative acceleration or deceleration): The object goes slower over time.
Changing direction: Even if the speed stays the same, changing direction means its velocity changes, which is acceleration.
Examples:
Speeding up: A car starting at a stop sign and picking up speed. A runner starting a race and getting faster.
Slowing down: A car going from 6 \text{ m/s} to 0 \text{ m/s} shows negative acceleration (slowing down).
Changing direction: A car turning a corner while keeping the same speed is still accelerating because its direction (part of its velocity) is changing.
Acceleration is a 'rate': It tells you how quickly velocity changes each second. Just like velocity, acceleration can change all the time.
Average acceleration concept: You can figure out the average acceleration over a certain time by looking at how much the velocity changed during that time.
Formula:
a{\text{avg}} = \frac{vf - v_i}{t}Units: Velocity is measured in meters per second (\text{m/s}); time is in seconds (\text{s}); so acceleration is measured in meters per second squared (\text{m/s}^2).
Important note: Acceleration isn't just about speeding up. It's any change in velocity, including slowing down or changing direction.
Another way to think about it: If a car accelerates by the same amount each second, its speed increases by that same amount each second (like going 0 \to 2 \to 4 \to 6 \text{ m/s}).
Page 4: Acceleration (Continued) and Examples
Positive acceleration example (Figure 4A): A car starts from v = 0 \text{ m/s} and gets faster over time at a steady rate. If its velocity increases by 2 \text{ m/s} every second, after 3 seconds its velocity will be 6 \text{ m/s}.
Negative acceleration example (Figure 4B): A car starts at v = 6 \text{ m/s} and slows down to 0 \text{ m/s} in 3 seconds. This means its velocity changed by -6 \text{ m/s} over 3 seconds.
Let's look at some numbers for steady acceleration:
Car speeding up by 2 \text{ m/s}^2: The car's velocity increases by 2 \text{ m/s} every second.
Car slowing down by 2 \text{ m/s}^2: The car's velocity decreases by 2 \text{ m/s} every second.
From the two examples:
From 0 \text{ m/s} to 6 \text{ m/s} in 3 \text{ s}
\rightarrow \text{acceleration } a = \frac{6 - 0}{3} = 2 \text{ m/s}^2From 6 \text{ m/s} to 0 \text{ m/s} in 3 \text{ s}
\rightarrow \text{acceleration } a = \frac{0 - 6}{3} = -2 \text{ m/s}^2
The sign of the acceleration (positive or negative) tells you if the object is speeding up (positive) or slowing down (negative).
Early note: Remember, acceleration is about how velocity changes, not just how speed changes. Direction is a part of velocity, so it's also a part of acceleration.
Summary statement: Acceleration tells us how fast and in what way an object's motion is changing over time.
Page 5: Average Acceleration and Calculations
Here's the formula to find the average acceleration over a certain time:
a{\text{avg}} = \frac{vf - v_i}{t}Units and what they mean:
Velocity is measured in \text{m/s}.
Time is measured in \text{s}.
So, acceleration is measured in \frac{\text{m/s}}{\text{s}} = \text{m/s}^2 (meters per second, per second).
Worked examples from the figures:
Example 1: The car starts from vi = 0 \text{ m/s} and gets to vf = 6 \text{ m/s} in t = 3 \text{ s}. The average acceleration is:
a_\text{avg} = \frac{6 - 0}{3} = 2 \text{ m/s}^2Example 2: The car slows from vi = 6 \text{ m/s} to vf = 0 \text{ m/s} in t = 3 \text{ s}. The average acceleration is:
a_\text{avg} = \frac{0 - 6}{3} = -2 \text{ m/s}^2
What do the results mean?:
A positive a\text{avg} means the speed is growing (getting faster) over that time. A negative a\text{avg} means the speed is decreasing (slowing down).
The number for a_\text{avg} (2 \text{ m/s}^2 in both examples) shows how much the velocity changes each second in these situations.
Key takeaway: The average acceleration formula gives us an easy way to figure out how quickly velocity changes over a certain time. It also works if the velocity changes in speed, direction, or both.
Note: In real life, acceleration can change all the time. So, the acceleration at one exact moment might be different from the average acceleration over a longer time.