Numericals of Motion
- Distance and Displacement:
- Distance (d) is the total path length covered.
- Displacement (s) is the shortest path from the initial to final point.
- Speed and Velocity:
- Speed (v) = Distance/Time (d/t).
- Velocity (v) = Displacement/Time (s/t).
- Acceleration:
- Acceleration (a) = Change in velocity/Time taken (Δv/t).
- Example: If a car's velocity changes from 20 m/s to 30 m/s in 5 seconds, a = (30-20)/5 = 2 m/s².
Force and Laws of Motion
- Newton's First Law:
- An object remains at rest or in uniform motion unless acted upon by an external force.
- Example: A book resting on a table stays at rest until pushed.
- Newton's Second Law:
- F = m × a (Force = mass × acceleration).
- Example: If a 5 kg object accelerates at 2 m/s², F = 5 × 2 = 10 N.
- Newton's Third Law:
- For every action, there is an equal and opposite reaction.
- Example: When you push off the ground, the ground pushes you upward with equal force.
Gravitation
- Universal Law of Gravitation:
- Every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Formula: F = G(m₁m₂)/r², where G is the gravitational constant (6.674 × 10⁻¹¹ N m²/kg²).
- Weight:
- Weight (W) = mass (m) × gravitational acceleration (g).
- On Earth, g ≈ 9.8 m/s².
- Example: A 10 kg object has a weight W = 10 × 9.8 = 98 N.
This concise guide summarizes the essential numericals of motion, force, and gravitation for Class 9 students, providing clear examples and formulas to aid understanding.