【Physics Basics】Motion of Objects: Study Guide
Hello! How is your physics study going? Many people feel that "physics is just endless calculations and sounds difficult," but don't worry. This chapter on "Motion of Objects" is actually very relatable—it’s simply about describing the "motion" we see in our everyday lives using words and equations.
Let’s start slowly by organizing our terminology. Once you master this, it will become a reliable source of points in your physics exams!
1. Speed and Velocity (What’s the difference?)
In daily life, we use "speed" and "velocity" interchangeably, but in physics, we distinguish them clearly. This is a common stumbling block for beginners, so let’s get it right from the start!
① Displacement and Distance
- Distance: The total length you have actually traveled (every step counts, even if you’re winding around).
- Displacement: A straight-line arrow showing "how far and in what direction" you are from the starting point to the destination.
② Speed and Velocity
In physics, "direction" is extremely important.
- Speed (Scalar): Just the rate of motion. We don't care about the direction.
- Velocity (Vector): A combination of "how fast" and "in which direction."
Formula:
\( v = \frac{\Delta x}{\Delta t} \) (Velocity = Displacement ÷ Time taken)
【Pro Tip!】
If a test question asks you to "find the velocity," it is a rule that you must include the direction, like "5.0 m/s in the positive direction"! Always provide the direction as part of your answer.
2. Relative Velocity (How does the other person look?)
This is the velocity of someone else as seen from your own perspective while you are also moving. It's the classic "looking at the train next to you while you're on a train" scenario.
The Trick to Thinking About It
Just subtract "your velocity" from "the other person's velocity"!
\( v_{AB} = v_B - v_A \)
(Velocity of B as seen from A = Velocity of B - Velocity of A)
【How to Remember】
Think of it as "Target (B) minus You (A)." By subtracting yourself, you are mentally shifting your frame of reference so that you are standing still.
Example: If your car is driving at 60 km/h and you are passed by a car going 80 km/h, the other car looks like it's moving at "80 - 60 = 20 km/h." That is relative velocity!
3. Acceleration (Changing your speed!)
Acceleration describes how much your speed increases (or decreases) over time.
Formula:
\( a = \frac{\Delta v}{\Delta t} \) (Acceleration = Change in velocity ÷ Time taken)
The unit is \( \text{m/s}^2 \) (meters per second squared).
【Fun Fact】
When acceleration is "negative," it means you are braking and slowing down. In physics, it’s easiest to remember "negative acceleration = deceleration."
4. Uniformly Accelerated Linear Motion (Most Important!)
This is the most common topic in entrance exams: motion in a straight line with constant acceleration. There are three main formulas, but don't just memorize them—try to understand what they mean first.
The 3 Magical Formulas
\( v_0 \): initial velocity, \( v \): final velocity, \( a \): acceleration, \( t \): time, \( x \): distance traveled (displacement)
- Velocity Equation: \( v = v_0 + at \) (You start at \( v_0 \) and get faster by \( a \) every second.)
- Distance Equation: \( x = v_0 t + \frac{1}{2}at^2 \) (Used to find the distance covered.)
- Time-Independent Equation: \( v^2 - v_0^2 = 2ax \) (Useful when the question doesn't give you the time \( t \))
【Common Mistake!】
It’s easy to forget the "\( \frac{1}{2} \)" in \( x = v_0 t + \frac{1}{2}at^2 \). If you visualize it as the area of a triangle on a graph (see the next section), it becomes much harder to forget why that half is there!
5. Reading Graphs (v-t Graphs)
If you see a graph in a physics motion problem, consider yourself lucky! Especially the v-t graph (vertical axis is velocity, horizontal axis is time)—it is a treasure trove of information.
- Slope: The slope of the line represents acceleration.
- Area: The area trapped between the graph line and the horizontal axis represents distance traveled (displacement).
【Pro Tip!】
Even if you forget the formulas, you can calculate the distance by sketching a v-t graph and finding the area. When in doubt, make it a habit to draw the graph!
6. Free Fall and Throwing (Gravity-based Motion)
This covers objects that are dropped or thrown. All you need to do is replace the acceleration \( a \) with the gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \)!
① Free Fall
Simply letting go of an object (\( v_0 = 0 \)).
\( v = gt \)
\( y = \frac{1}{2}gt^2 \)
② Vertical Throw Downward
Throwing an object downwards with force. You now have an initial velocity \( v_0 \).
③ Vertical Throw Upward
Throwing an object upwards. The key characteristic is that "at the highest point, velocity \( v = 0 \)."
If you set the upward direction as positive, gravity is pulling downwards, so the acceleration will be \( -g \).
【It might feel difficult at first, but you've got this...】
If you get confused by the negative signs in throwing-upward problems, just think simply: "The direction you are going (up) is positive, and the thing getting in your way (gravity/down) is negative."
Summary: Key Points of This Chapter
・For "velocity" and "displacement," direction is key!
・Relative velocity is "Target minus You"!
・Learn to use the three formulas for uniformly accelerated motion!
・The area of a v-t graph is "distance"!
Great job! This field becomes like solving a puzzle once you repeat the practice problems. Try tackling the basic examples first!