Kinematics

Rest: A body is said to be at rest if it does not change its position with respect to its surroundings. (e.g., A book lying on a table).

Motion: A body is said to be in motion if it changes its position with respect to its surroundings. (e.g., A moving car).

Note: State of rest or motion is relative. A passenger in a moving bus is at rest w.r.t fellow passengers but in motion w.r.t an observer outside.

• Translatory Motion: Motion in which a body moves without any rotation.
  - Linear: Straight line motion (e.g., free-falling object).
  - Circular: Motion along a circular path (e.g., Toy train on circular track).
  - Random: Irregular motion (e.g., Flight of butterflies).
• Rotatory Motion: Spinning motion of a body about its axis (e.g., Wheel of a car, Steering wheel).
• Vibratory Motion: To and fro motion of a body about its mean position (e.g., Pendulum of a clock, See-saw).

Physical quantities which can be completely described by their magnitude only.
Examples: Mass, Length, Time, Speed, Temperature, Volume, Energy.

Physical quantities which are described completely by their magnitude and direction.
Examples: Velocity, Force, Displacement, Momentum, Torque.

• Symbolic: Represented by bold letters (F, a) or letters with a bar/arrow over them ($\vec{F}$).
• Graphical: Represented by a straight line with an arrowhead. Length of line represents magnitude (scale), and arrowhead points in the direction.

• Position: The location of a place or a point with respect to some reference point (origin).
• Distance ($S$): Length of a path between two points. It is a scalar quantity. Unit: metre ($m$).
• Displacement ($d$): Shortest distance between two points which has magnitude and direction. It is a vector quantity. Unit: metre ($m$).

• Speed ($v$): The distance covered by an object in unit time.
  Formula: $v = \frac{S}{t}$
  Unit: $ms^{-1}$ (Scalar).
• Velocity ($\vec{v}$): The rate of displacement of a body.
  Formula: $\vec{v} = \frac{\vec{d}}{t}$
  Unit: $ms^{-1}$ (Vector).
• Uniform Velocity: If a body covers equal displacement in equal intervals of time.

Acceleration ($a$): The rate of change of velocity of a body.
Formula: $a = \frac{v_f - v_i}{t}$
Unit: $ms^{-2}$ (Vector).

• Positive Acceleration: If velocity increases with time (direction same as velocity).
• Negative Acceleration (Retardation/Deceleration): If velocity decreases with time (direction opposite to velocity).
• Uniform Acceleration: If velocity changes by equal amounts in equal intervals of time.

A graph plotted between time (x-axis) and distance (y-axis).

• Object at Rest: Horizontal line parallel to time axis.
• Constant Speed: Straight line with a constant slope rising from origin.
• Variable Speed: Curved line. The slope (tangent) at any point gives speed.

A graph plotted between time (x-axis) and speed (y-axis).

• Object at Rest: Line on the time axis (v=0).
• Constant Speed: Horizontal line parallel to time axis.
• Uniform Acceleration: Straight line with positive slope. The gradient gives acceleration.
• Distance Traveled: The area under the Speed-Time graph represents the distance covered.

Relates initial velocity ($v_i$), final velocity ($v_f$), acceleration ($a$), and time ($t$). derived from the slope of Speed-Time graph.

Formula: $v_f = v_i + at$

Relates distance ($S$), initial velocity ($v_i$), acceleration ($a$), and time ($t$). Derived from the area under Speed-Time graph (Rectangle + Triangle).

Formula: $S = v_i t + \frac{1}{2}at^2$

Relates velocity, distance, and acceleration (independent of time). Derived from the total area of trapezium under Speed-Time graph.

Formula: $2aS = v_f^2 - v_i^2$

When a body falls freely under gravity, it moves with uniform acceleration towards the center of Earth. This is called Gravitational Acceleration ($g$).

• Value of $g$ on Earth $\approx 10 ms^{-2}$ (approx).
• Downward Motion: $g$ is positive ($+10 ms^{-2}$).
• Upward Motion: $g$ is negative ($-10 ms^{-2}$).

• $v_f = v_i + gt$
• $h = v_i t + \frac{1}{2}gt^2$
• $2gh = v_f^2 - v_i^2$