Kinematics describes motion without analyzing the forces causing it. It deals with displacement, velocity, acceleration, and time. There are two main categories covered: rectilinear (1D) and projectile (2D) motion.

Rectilinear Motion uses the three SUVAT equations (valid only for constant acceleration): v = u + at, s = ut + (1/2)at^2, and v^2 = u^2 + 2as. The displacement in the nth second is s_n = u + a(2n-1)/2. For variable acceleration, calculus is essential: v = ds/dt, a = dv/dt = v(dv/ds).

Projectile Motion decomposes into independent horizontal (a_x = 0) and vertical (a_y = -g) components. Key results: Time of flight T = 2usin(theta)/g, Maximum height H = u^2sin^2(theta)/(2g), Range R = u^2sin(2theta)/g. Maximum range occurs at theta = 45 degrees. Complementary angles give equal range but different heights and flight times.

Relative Motion uses v_{A/B} = v_A - v_B. River crossing problems require vector decomposition of swimmer/boat velocity.

Graph Analysis connects position, velocity, and acceleration through slopes (derivatives) and areas (integrals). The slope of x-t gives velocity; area under v-t gives displacement.

Key JEE traps include: confusing distance with displacement, forgetting sign conventions, assuming a = 0 when v = 0, and using SUVAT for variable acceleration.