SUVAT equations cover all constant-acceleration problems. Each omits one variable: (1) $v = u + at$ omits $s$; (2) $s = ut + \frac{1}{2}at^2$ omits $v$; (3) $v^2 = u^2 + 2as$ omits $t$.

Displacement in nth second is $s_n = u + \frac{a(2n-1)}{2}$. This is NOT total displacement — it is the displacement during that single second.

Free fall sign convention: If upward is positive, $g = -9.8$ m/$s^{2}$. If downward is positive, $g = +9.8$ m/$s^{2}$. Never mix conventions within a problem.

Projectile time of flight: $T = \frac{2u\sin\theta}{g}$. Time to reach peak = $T/2 = \frac{u\sin\theta}{g}$.

Projectile max height: $H = \frac{u^2\sin^2\theta}{2g}$. Proportional to $\sin^2\theta$.

Projectile range: $R = \frac{u^2\sin 2\theta}{g}$. Maximum at $\theta = 45°$; $R_{max} = u^2/g$.

Complementary angles: $\theta$ and $(90° - \theta)$ always produce identical range. Heights ratio: $H_{\theta_2}/H_{\theta_1} = \tan^2\theta_2/\tan^2\theta_1$. For 60° vs 30°: $H_{60}/H_{30} = 3$.

Highest point of projectile: $v_y = 0$, but $v_x = u\cos\theta$ remains unchanged. Speed at peak = $u\cos\theta$ — minimum speed, not zero.

v-t graph: slope = acceleration; area under curve = displacement (not distance).

x-t graph: slope = velocity; area has no direct physical meaning.

Centripetal acceleration: $a_c = v^2/r = \omega^2 r$; directed toward centre; $[M^0L^1T^{-2}]$.

Angular velocity: $\omega = v/r$; unit rad/s; $[M^0L^0T^{-1}]$.

Uniform circular motion: speed = constant; velocity direction = continuously changing; acceleration = $a_c$ toward centre.