[Physics Basics] Motion of Objects: Master the Fundamentals!
Hello there! How is your physics study going? Many people feel that "Physics involves so many calculations and seems really difficult." But don't worry! This chapter on the "Motion of Objects" is actually a very simple field where we just express the movements around us using numbers.
A bicycle picking up speed, a ball being thrown into the sky... Let's look at these everyday occurrences through the lens of physics together!
1. What's the difference between "Speed" and "Velocity"?
In daily life, these words are often used interchangeably, but in the world of physics, there is a clear distinction. This is the first place many students stumble, so let's get it organized!
① Distance and Displacement
・Distance: The total length of the path actually traveled (a scalar quantity).
・Displacement: The length and direction of a "straight line" connecting the start point to the end point (a vector quantity).
(Example: If you run 100m and return to the starting spot, the distance is 200m, but your displacement is "0"!)
② Speed and Velocity
・Speed: How fast something is moving (magnitude only).
・Velocity: How fast something is moving and in which direction (magnitude and direction).
In physics, "direction" is very important. If we define the rightward direction as positive (+), then leftward is expressed as negative (-).
[Formula] Uniform Linear Motion
This describes motion where an object moves in a straight line at a constant speed.
\( x = vt \)
( \( x \): distance traveled [m], \( v \): speed [m/s], \( t \): time [s] )
★Pro-tip:
The unit [m/s] is read as "meters per second." It represents "how many meters you travel in one second."
2. What is Acceleration?
Acceleration is the numerical value that represents the state where "speed gradually increases."
For example, when a car starts moving and gains speed, acceleration is being produced.
[Formula] Acceleration \( a \)
\( a = \frac{v - v_0}{t} \)
( \( v_0 \): initial velocity [m/s], \( v \): final velocity [m/s], \( t \): time elapsed [s] )
The unit is \( [m/s^2] \) (meters per second squared). The square signifies "how many [m/s] the speed changes by every second."
[Key Point!]
・When speed increases: acceleration is positive (+)
・When braking/slowing down: acceleration is negative (-)
3. Most Important! The 3 Formulas of Uniformly Accelerated Linear Motion
For motion where acceleration is constant (motion where the speed changes at a steady rate), there are 3 formulas that are guaranteed to appear on tests. They might feel tricky at first, but try memorizing them like a chant!
① When you want to find velocity:
\( v = v_0 + at \)
② When you want to find distance (displacement):
\( x = v_0 t + \frac{1}{2}at^2 \)
③ When you don't know the time \( t \):
\( v^2 - v_0^2 = 2ax \)
[Common Mistake: Choosing the Right Formula]
When you aren't sure which formula to use, look at the problem statement and write down "what you know and what you want to find."
・If you know the time: Use ① or ②
・If you don't know the time: Use ③
Doing just this will significantly reduce your confusion!
4. Free Fall and Vertical Throw (Motion under Gravity)
Motion involving dropping or throwing objects is actually a type of "Uniformly Accelerated Linear Motion." The only difference is that acceleration becomes the gravitational acceleration \( g = 9.8 [m/s^2] \)!
① Free Fall
This is the motion of dropping an object by letting go. Since the initial velocity \( v_0 = 0 \), the formulas become simple:
・Velocity: \( v = gt \)
・Distance: \( y = \frac{1}{2}gt^2 \)
② Vertical Throw Downward
This is the motion of throwing something straight down with force. Since there is an initial velocity \( v_0 \), you simply substitute \( a \) with \( g \) in the standard formulas.
③ Vertical Throw Upward
This is the motion of throwing something straight up. The trick is to define "upward as positive"!
・Since gravity acts downward, the acceleration becomes \( a = -g \) (negative).
・At the highest point, the velocity \( v \) is 0 for an instant. This is the biggest hint for solving these problems!
5. Summary: Remember these key takeaways!
・Velocity has a "direction." Use a negative sign for the opposite direction!
・The area under the graph (v-t graph) represents the distance traveled!
・For the 3 formulas, write down the known values before plugging them in!
・Gravitational acceleration is \( 9.8 [m/s^2] \). Be careful with the negative sign during upward throws!
Physics motion is like a puzzle. Once you memorize the basic pieces (the formulas) and apply the hints from the problem, you will definitely be able to solve them.
Start by challenging yourself with simple calculation problems and get the feeling of saying, "I solved it!" I'm rooting for you!