}]]}]}]}] 30:T2374,

### Motion - **Definition:** Change in position of an object with respect to time. - **Types of Motion:** - **Uniform Motion:** Constant velocity, zero acceleration. - **Non-Uniform Motion:** Changing velocity, non-zero acceleration. - **Key Terms & Formulas:** - **Distance (d):** Total path length covered. Scalar quantity. Unit: meter (m). - **Displacement (s):** Shortest distance from initial to final position. Vector quantity. Unit: meter (m). - **Speed (v):** Distance covered per unit time. $v = \frac{d}{t}$. Scalar. Unit: m/s. - **Velocity ($\vec{v}$):** Displacement per unit time. $\vec{v} = \frac{\vec{s}}{t}$. Vector. Unit: m/s. - **Acceleration ($\vec{a}$):** Rate of change of velocity. $\vec{a} = \frac{\vec{v} - \vec{u}}{t}$. Vector. Unit: m/s$^2$. - Positive acceleration: Velocity increases. - Negative acceleration (retardation/deceleration): Velocity decreases. - **Equations of Motion (for uniformly accelerated motion):** 1. $v = u + at$ 2. $s = ut + \frac{1}{2}at^2$ 3. $v^2 = u^2 + 2as$ Where: $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $t$ = time, $s$ = displacement. - **Graphical Representation:** - **Distance-Time Graph:** - Slope = Speed. - Straight line = Uniform speed. - Curved line = Non-uniform speed. - **Velocity-Time Graph:** - Slope = Acceleration. - Area under graph = Displacement. - Straight line (constant slope) = Uniform acceleration. - Horizontal line = Uniform velocity (zero acceleration). - Curved line = Non-uniform acceleration. ### Force and Laws of Motion - **Force:** An external agent that can change or tend to change the state of rest or motion of an object. Unit: Newton (N). - **Balanced Forces:** Net force is zero; does not cause change in state of motion. - **Unbalanced Forces:** Net force is non-zero; causes change in state of motion (acceleration). - **Newton's Laws of Motion:** 1. **First Law (Law of Inertia):** An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. - **Inertia:** Tendency of an object to resist changes in its state of motion. - Inertia of Rest: Resists change from rest. - Inertia of Motion: Resists change from motion. - Inertia of Direction: Resists change in direction. - Mass is a measure of inertia. 2. **Second Law:** The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force. - $F = ma$ (Force = mass $\times$ acceleration) - **Momentum ($\vec{p}$):** Product of mass and velocity. $\vec{p} = m\vec{v}$. Vector. Unit: kg m/s. - Change in momentum: $\Delta p = m(v-u)$. 3. **Third Law:** To every action, there is an equal and opposite reaction. - Forces always occur in pairs. Action and reaction forces act on different bodies. - **Conservation of Momentum:** In an isolated system (no external forces), the total momentum before and after an interaction remains constant. - $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$ - Applications: Recoil of a gun, collisions. ### Gravitation - **Universal Law of Gravitation (Newton):** Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. - $F = G \frac{m_1 m_2}{r^2}$ - $G$ = Universal Gravitational Constant = $6.67 \times 10^{-11} \text{ Nm}^2/\text{kg}^2$. - **Free Fall:** Mo