Motion in One Dimension

Subtopics Covered

• Motion under gravity
• Distance and Displacement

Key Concepts Discussed

• Motion in a straight line
• Important aspects of motion
• Velocity and Acceleration
• Acceleration due to gravity

Key Points

• Graph Rules:
  • Time cannot be negative.
  • Displacement cannot decrease.
  • Speed cannot be negative.
  • Two positions cannot exist at the same time.
• Velocity (v): Determined from the slope of Distance-Time graph.
• Acceleration (a): Determined from the slope of the Velocity-Time graph.
• Area under the velocity-time graph: Gives displacement.

Important Formulas:

1. Conversions:

• From km/hr to m/s: multiply by 5/18.
• From m/s to km/hr: multiply by 18/5.

2. Kinematic Equations:

• v = u + at
• s = ut + (1/2)at^2
• v² = u² + 2as

3. For instantaneous values: Specific point in time.
4. For average values: Over an interval of time.
5. Distance vs Displacement:

• Scalar vs Vector
• Total path vs Shortest path

6. g = 9.8 m/s² (approx 10 m/s²)

• For free fall
  • v = u + gt
  • s = ut + (1/2)gt^2
  • v² = u² + 2gs

Practical Applications Covered:

• Free fall problems
  • Concepts of Drop vs Throw
• Projectile motion

Galileo’s Law of Odd Numbers

• Use of X, 3X, 5X pattern in problems

Graph Analysis

1. Distance-Time Graph

• Slope = speed
• Area under the curve = displacement

2. Velocity-Time Graph

• Slope = acceleration
• Area under the curve = displacement

3. Acceleration-Time Graph

• Area under the curve = change in velocity

Problem-Solving Strategies:

• Conceptual and numerical problems discussed
• Important questions and problem patterns likely in exams