Quick Revision Notes: Motion (Class 9 Science - MP Board)

1. Introduction to Motion

State of Rest: An object is said to be at rest if it does not change its position with respect to its surroundings with time.
State of Motion: An object is said to be in motion if it changes its position with respect to its surroundings with time.
Motion is relative: The motion of an object depends on the observer. For example, passengers inside a moving bus are at rest relative to each other, but in motion relative to a person standing outside on the road.

Scalar Quantities: Physical quantities that have magnitude only, but no specific direction. (e.g., Distance, Speed, Mass, Time).
Vector Quantities: Physical quantities that have both magnitude and direction. (e.g., Displacement, Velocity, Acceleration, Force).

Distance: The actual length of the path covered by a moving object, regardless of the direction.
- S.I. Unit: Meter (m)
- It is a scalar quantity.
- Distance can never be zero or negative for a moving object (Always > 0).
Displacement: The shortest straight-line distance between the initial position and the final position of an object.
- S.I. Unit: Meter (m)
- It is a vector quantity.
- Displacement can be positive, negative, or zero.

Speed: The distance traveled by an object per unit time.
- Speed = Distance / Time (v = s / t)
- S.I. Unit: Meter per second (m/s or m s^-1)
- It is a scalar quantity.
Velocity: The speed of an object in a specified direction (displacement per unit time).
- Velocity = Displacement / Time (v = d / t)
- S.I. Unit: Meter per second (m/s)
- It is a vector quantity.
Average Speed: Total distance traveled divided by total time taken.
- Average Speed = Total Distance Traveled / Total Time Taken
Average Velocity: For uniformly changing velocity, it is the arithmetic mean of initial and final velocity.
- Average Velocity = (Initial Velocity + Final Velocity) / 2 -> v_avg = (u + v) / 2

Acceleration: The rate of change of velocity with respect to time.
- Acceleration = (Final Velocity - Initial Velocity) / Time
- Formula: a = (v - u) / t
- S.I. Unit: Meter per second square (m/s^2 or m s^-2)
- It is a vector quantity.
Uniform Acceleration: When an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time.
Non-uniform Acceleration: When velocity changes by unequal amounts in equal intervals of time.
Retardation / Deceleration: Negative acceleration (when velocity decreases with time).

Slope of v-t graph gives the Acceleration of the object.
Area under v-t graph gives the Displacement / Distance traveled by the object.
Straight line parallel to time axis = Uniform Velocity (Acceleration = 0).
Straight inclined line = Uniform Acceleration.

For an object moving with initial velocity u, final velocity v, acceleration a, time t, and distance/displacement s:

When an object moves in a circular path with a uniform speed, its motion is called Uniform Circular Motion.
Even though the speed is constant, the velocity changes continuously because the direction of motion changes at every point. Therefore, it is an accelerated motion.
Formula for speed in circular motion: Speed = Circumference / Time -> v = (2 * pi * r) / t (where r is the radius of the circular path)

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