📐 The Science of Motion
🔍 Remember your observations: The moving bus, falling leaf, and thrown ball. Now let's understand the science behind them.
1. Rest and Motion are Relative
Key Insight: An object is at rest if its position doesn't change with time relative to its surroundings. It's in motion if its position changes.
📌 Connecting to Observation 1:
When you're in the moving bus:
- Relative to bus: You are at rest (your position on the bus doesn't change)
- Relative to ground: You are in motion (your position relative to trees changes)
- Relative to you: Trees appear to move backwards (they are in motion relative to you)
🧠 Think Deeper: Is there any object that is absolutely at rest? Everything in the universe is moving - the Earth rotates, orbits the Sun, the Sun moves in the galaxy!
2. Distance vs Displacement
Distance = Total path length traveled
Displacement = Shortest straight line from start to end
Displacement has direction, distance does not
📌 Example:
If you walk 5 meters north, then 5 meters south back to start:
- Distance traveled: 5 + 5 = 10 meters
- Displacement: 0 meters (you're back where you started)
Units: Both measured in meters (m), kilometers (km), etc.
3. Speed vs Velocity
Speed = Distance / Time
Velocity = Displacement / Time
Velocity has direction, speed does not
📌 Connecting to Observation 2:
The falling leaf:
- Its speed changes as it falls (speeds up, slows down due to air)
- Its velocity constantly changes direction (zigzag path means changing velocity)
Units: meters per second (m/s), kilometers per hour (km/h)
4. Acceleration
Acceleration = Change in velocity / Time taken
a = (v - u) / t
where u = initial velocity, v = final velocity, t = time
📌 Connecting to Observation 3:
The ball thrown upward:
- Going up: Velocity decreases (deceleration = negative acceleration)
- At the top: Velocity becomes 0 for an instant
- Coming down: Velocity increases (acceleration)
- The acceleration due to gravity (g = 9.8 m/s²) is constant throughout!
Units: meters per second squared (m/s²)
🧠 Think Deeper: Can an object have zero velocity but still be accelerating? Yes! At the top of its throw, the ball has zero velocity but is still accelerating downward due to gravity.
5. Equations of Motion (Constant Acceleration)
1. v = u + at
2. s = ut + ½at²
3. v² = u² + 2as
where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time
📌 Example Problem:
A car starts from rest (u = 0) and accelerates at 2 m/s² for 10 seconds. Find its final velocity and distance covered.
Solution:
- v = u + at = 0 + (2)(10) = 20 m/s
- s = ut + ½at² = 0 + ½(2)(10)² = ½(2)(100) = 100 m
📊 Quick Reference
| Quantity |
Definition |
Formula |
Unit |
| Distance |
Total path length |
- |
m |
| Displacement |
Shortest distance (with direction) |
- |
m |
| Speed |
Distance/Time |
s = d/t |
m/s |
| Velocity |
Displacement/Time |
v = s/t |
m/s |
| Acceleration |
Change in velocity/Time |
a = (v-u)/t |
m/s² |
🧠 Critical Thinking Challenge:
If you drop a feather and a hammer on Earth, they fall at different rates. But on the moon, they fall together. Why? (Hint: Think about what's different between Earth and moon)
Try to reason it out before looking up the answer. This is what scientists do!