Part 1: Scalars, Vectors, and Motion Basics

Kinematics begins with the distinction between scalar and vector quantities. Scalars (distance, speed, time, mass, energy) have magnitude only. Vectors (displacement, velocity, acceleration, force) have magnitude and direction. Displacement is the vector from start to finish regardless of path; distance is the total path length. Vector resolution uses $A_x = A\cos\theta$ and $A_y = A\sin\theta$ where $\theta$ is measured from the positive x-axis. The dot product of two vectors is $\vec{A}\cdot\vec{B} = AB\cos\theta$ (scalar); the magnitude of the cross product is $|\vec{A}\times\vec{B}| = AB\sin\theta$ (vector perpendicular to both).

Part 2: Equations of Motion

For any motion with constant acceleration, exactly three core SUVAT equations apply. Each links four of the five kinematic variables and omits one. Selecting the equation that omits the unknown saves time in NEET. The displacement in the nth second, $s_n = u + \frac{a(2n-1)}{2}$, is a derived result often tested as a standalone formula. Dimensional homogeneity must hold for every equation. Free fall is a special case with $a = g$ (direction depends on sign convention).

Part 3: Graphical Kinematics

The two most important graphs are x-t (position vs time) and v-t (velocity vs time). On an x-t graph: slope = instantaneous velocity; a straight line means constant velocity; a curve means changing velocity. On a v-t graph: slope = acceleration; a horizontal line means constant velocity (zero acceleration); area under curve = displacement (positive above axis, negative below). Acceleration-time graphs are less common in NEET but are the derivative of v-t graphs.

Part 4: Projectile Motion

Projectile motion treats horizontal and vertical components independently. Horizontally: constant velocity $u\cos\theta$ (no air resistance). Vertically: initial velocity $u\sin\theta$, decelerating under gravity until peak (where $v_y = 0$), then accelerating downward. Formulas: $T = 2u\sin\theta/g$; $H = u^2\sin^2\theta/2g$; $R = u^2\sin 2\theta/g$. At $\theta = 45°$, range is maximum. Complementary angles share range; the larger angle yields 3× the height when compared with its 60°/30° complement. At the peak, speed = $u\cos\theta$ (minimum, not zero).

Part 5: Uniform Circular Motion

Circular motion at constant speed involves continuous change in velocity direction. Angular velocity $\omega = v/r$ relates linear speed to angular speed. Centripetal acceleration $a_c = v^2/r = \omega^2 r$ is directed toward the centre and is responsible for the change in direction. No tangential acceleration exists in uniform circular motion. Speed stays constant; velocity (a vector) does not.