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 + \frac{1}{2}$$at^2, and $v^2$ = $u^2$ + 2as. The displacement in the nth second is $s_n$ = u + a$\frac{2n-1}{2}$. For variable acceleration, calculus is essential: v = $\frac{ds}{dt}$, a = $\frac{dv}{dt}$ = v$\frac{dv}{ds}$.

Projectile Motion decomposes into independent horizontal ($a_x$ = 0) and vertical ($a_y$ = -g) components. Key results: Time of flight T = 2usin$\frac{theta}{g}$, Maximum height H = $u^2$sin^2$$\frac{theta}{(2g)}, Range R = $u^2$*sin$\frac{2*theta}{g}$. 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.