Mind map :: Chpater 8 : Motion

Motion

Distance and Displacement

Distance: Total path length (scalar quantity).

Displacement: Shortest path from initial to final position (vector quantity).

Example: A car moving in a circle has distance > displacement.

Real-life Example: If you walk 10 meters east and then 10 meters west, your distance is 20 meters, but your displacement is 0 meters.

Speed and Velocity

Speed: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \) (scalar).

Velocity: \( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \) (vector).

Example: A car moving at 60 km/h has speed = 60 km/h, velocity = depends on direction.

Real-life Example: A cyclist moving at 15 km/h north has a velocity of 15 km/h north, but their speed is 15 km/h.

Average Speed: \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \).

Average Velocity: \( \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \).

Acceleration

Acceleration: \( \text{Acceleration} = \frac{\Delta v}{\Delta t} \).

Positive Acceleration: Speeding up.

Negative Acceleration (Deceleration): Slowing down.

Example: A car accelerates from 0 to 60 km/h in 10 seconds.

Real-life Example: A rocket launching into space experiences positive acceleration.

Uniform Acceleration: Constant change in velocity over time.

Non-Uniform Acceleration: Changing rate of acceleration.

Uniform and Non-Uniform Motion

Uniform Motion: Constant speed in a straight line.

Non-Uniform Motion: Changing speed or direction.

Example: A car moving at 60 km/h (uniform) vs. a car speeding up (non-uniform).

Real-life Example: A train moving at a constant speed (uniform) vs. a car in city traffic (non-uniform).

Graphical Representation: Uniform motion is a straight line on a distance-time graph.

Graphical Representation

Distance-Time Graph: Slope = Speed.

Distance-Time Graph

Slope of the graph = Speed.

• Straight line: Uniform motion (constant speed).
• Curved line: Non-uniform motion (changing speed).

Example: A car moving at a constant speed will have a straight line on a distance-time graph.

Velocity-Time Graph: Slope = Acceleration.

Velocity-Time Graph

Slope of the graph = Acceleration.

• Straight line: Uniform acceleration.
• Curved line: Non-uniform acceleration.

Area under the graph = Displacement.

Example: A car accelerating uniformly will have a straight line with a positive slope on a velocity-time graph.

Speed-Time Graph: Similar to Velocity-Time Graph but without direction.

Speed-Time Graph

Slope of the graph = Rate of change of speed.

• Straight line: Uniform change in speed.
• Curved line: Non-uniform change in speed.

Example: A car increasing its speed uniformly will have a straight line with a positive slope on a speed-time graph.

Equations of Motion

1. \( v = u + at \)

2. \( s = ut + \frac{1}{2}at^2 \)

3. \( v^2 = u^2 + 2as \)

Example: A car starts from rest (\( u = 0 \)) and accelerates at \( 2 \, \text{m/s}^2 \) for 5 seconds.

Real-life Example: A ball thrown upward slows down due to gravity (negative acceleration).

Derivation of Equations: Explain how the equations are derived from basic principles.