Chapter 7: Motion

1. Describing Motion

• Motion and Reference Points: Motion is a change in the position of an object over time. To describe the position of an object, we must specify a reference point, also known as the origin.
• Motion Along a Straight Line: This is the simplest type of motion.
  • Distance: The total path length covered by an object irrespective of direction. It is a physical quantity that has only magnitude (numerical value).
  • Displacement: The shortest distance measured from the initial position to the final position of an object. It has both magnitude and direction.
• Zero Displacement: An object can have zero displacement even if the distance covered is not zero (e.g., if an object travels and returns to its starting point).

2. Types of Motion

• Uniform Motion: When an object covers equal distances in equal intervals of time.
• Non-Uniform Motion: When an object covers unequal distances in equal intervals of time (e.g., a car moving in traffic).

3. Measuring the Rate of Motion

• Speed: The distance travelled by an object in unit time.
  • SI Unit: Metre per second (m s⁻¹ or m/s).
  • Average Speed: Since speed is often not constant, we calculate average speed as:
    Average Speed = Total distance travelled / Total time taken
• Velocity (Speed with Direction): Velocity is the speed of an object moving in a definite direction.
  • It changes if the object's speed, direction, or both change.
  • Average Velocity: Can be calculated as the displacement divided by the total time. If velocity changes at a uniform rate, it is the arithmetic mean of initial and final velocity:
    Average Velocity = (Initial velocity + Final velocity) / 2

4. Rate of Change of Velocity (Acceleration)

• Acceleration: A measure of the change in the velocity of an object per unit time.
• Formula:
  a = (v - u) / t
  Where a is acceleration, v is final velocity, u is initial velocity, and t is time.
• SI Unit: m s⁻² (meter per second squared).
• Types of Acceleration:
  • Uniform Acceleration: Velocity changes by equal amounts in equal time intervals (e.g., a freely falling body).
  • Non-Uniform Acceleration: Velocity changes by unequal amounts in equal time intervals.
• Acceleration is considered positive if it is in the direction of velocity and negative if it is opposite to the direction of velocity.

5. Graphical Representation of Motion

• Distance-Time Graphs:
  • Show the change in position over time.
  • Straight line: Indicates uniform speed.
  • Curved line: Indicates non-uniform speed.
  • The slope of a distance-time graph represents the speed of the object.
• Velocity-Time Graphs:
  • Show the variation of velocity with time.
  • Straight line parallel to time axis: Uniform motion (constant velocity).
  • Straight line with a slope: Uniform acceleration.
  • The area under the velocity-time graph represents the distance (magnitude of displacement) travelled by the object.

6. Equations of Motion

For objects moving along a straight line with uniform acceleration, three key equations relate velocity, acceleration, time, and distance:

Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance.

7. Uniform Circular Motion

• Definition: When an object moves in a circular path with uniform speed.
• Accelerated Motion: Even though the speed is constant, the velocity changes continuously because the direction of motion changes at every point. Therefore, uniform circular motion is an accelerated motion.
• Formula: If an object takes time t to complete one round of a circular path of radius r, the velocity v is:
  v = 2πr / t
• Examples: The motion of the moon around the earth, a satellite in orbit, or a cyclist on a circular track. The direction of motion at any instant is tangential to the circle.