Motion & Energy

Distance vs. Displacement:
- Distance is a scalar quantity measuring the total path length traveled by an object, regardless of direction.
- Displacement is a vector quantity measuring the straight-line distance and direction from an object's initial position to its final position.
Speed vs. Velocity:
- Speed is the rate at which an object covers distance (scalar): $v = \frac{d}{t}$
- Velocity is the rate of change of displacement in a given direction (vector): $v = \frac{\Delta s}{t}$
Acceleration:
- The rate of change of velocity over time: $a = \frac{v - u}{t}$
- Where $a$ is acceleration ( $\text{m/s}^2$ ), $v$ is final velocity ( $\text{m/s}$ ), $u$ is initial velocity ( $\text{m/s}$ ), and $t$ is time taken ( $\text{s}$ ).
  1.2 Newton's Laws of Motion

First Law (Law of Inertia):
- An object will remain at rest or continue to move at a constant velocity in a straight line unless acted upon by an external net unbalanced force.
Second Law ( $F = m \times a$ ):
- The acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass: $F = m \times a$
- Where $F$ is net force ( $\text{N}$ ), $m$ is mass ( $\text{kg}$ ), and $a$ is acceleration ( $\text{m/s}^2$ ).
Third Law (Action-Reaction):
- For every action force, there is an equal and opposite reaction force acting on different interacting objects.

Kinetic Energy ( $E_k$ ):
- Energy possessed by an object due to its motion: $E_k = \frac{1}{2} \times m \times v^2$
n ( $E_p$ ):
- Stored energy resulting from an object's position in a gravitational field: $E_p = m \times g \times h$
- Where $g \approx 9.8\,\text{m/s}^2$ and $h$ is height above the reference point ( $\text{m}$ ).
Work Done:
- The amount of energy transferred when a force moves an object across a displacement: $W = F \times d$
Law of Conservation of Energy:
- Energy cannot be created or destroyed; it can only be transferred between objects or transformed from one form to another.
- In a closed system, total mechanical energy is conserved: $E_{\text{total}} = E_k + E_p$

Definition: The primary mechanism of biological evolution proposed by Charles Darwin and Alfred Russel Wallace, by which organisms better adapted to their environment tend to survive and produce more offspring.
Key Steps of Natural Selection:
1. Variation: Individuals within a population exhibit phenotypic variation caused by random genetic mutations and sexual reproduction.
2. Selection Pressure: Environmental challenges (such as predators, competition for resources, drought, or disease) create a struggle for existence.
3. Differential Survival and Reproduction: Individuals possessing favorable traits (adaptations) better suited to the environment have higher survival and reproductive rates.
4. Inheritance: Favorable alleles are passed down to offspring, increasing in frequency within the population over successive generations.

The Fossil Record:
- Reveals structural transitions and chronologically ordered changes in organisms over geological epochs.
- Transitional fossils demonstrate intermediate anatomical stages between ancestral and modern species.
Comparative Anatomy:
- Homologous Structures: Anatomical features that share a common evolutionary origin despite differing in function (e.g., the pentadactyl limb in humans, bats, and whales), evidencing divergent evolution.
- Analogous Structures: Features that serve similar functions but evolved independently through different evolutionary lineages due to similar environmental pressures (e.g., bird wings and insect wings), evidencing convergent evolution.
- Vestigial Structures: Reduced remnants of functional structures inherited from ancestors that no longer serve a vital function (e.g., human tailbone, pelvic bones in whales).
Biochemical and Genetic Evidence:
- All living organisms share the same basic genetic code composed of nucleic acids ( $\text{DNA}$ and $\text{RNA}$ ).
- The degree of similarity in amino acid or nucleotide sequences correlates directly with evolutionary closeness and time elapsed since sharing a common ancestor.
Comparative Embryology:
- Shared developmental structures in vertebrate embryos (such as pharyngeal arches and post-anal tails) point to a shared evolutionary ancestry.

Definition: The evolutionary process by which biological populations evolve to become distinct, reproductively isolated species.
Mechanism of Allopatric Speciation:
1. Geographic Isolation: A single population is separated by a physical barrier (e.g., a river, mountain, or ocean).
2. Independent Mutation and Selection: The isolated populations face different environmental conditions and selection pressures, leading to divergent adaptations.
3. Reproductive Isolation: Accumulated genetic differences prevent the two groups from interbreeding to produce viable, fertile offspring if they come back into contact.