Cornell Notes — Kinematics Full Topic — Notes | NoteTube

Cue / Question	Notes
What are the 3 equations of motion?	v = u + at; s = ut + ½ $at^{2}$ ; $v^{2}$ = $u^{2}$ + 2as
What does each equation omit?	1st omits s; 2nd omits v; 3rd omits t
Formula for displacement in nth second?	$s_n = u + \frac{a(2n-1)}{2}$ — unit: m
Projectile: Time of flight formula?	$T = \frac{2u\sin\theta}{g}$ — depends on sin θ
Projectile: Max height formula?	$H = \frac{u^2\sin^2\theta}{2g}$ — depends on s $in^{2}$ θ
Projectile: Range formula?	$R = \frac{u^2\sin 2\theta}{g}$ — max at θ = 45°
Complementary angles property?	θ and (90°−θ) give same range R; H ratio = t $an^{2}$ θ
Velocity at highest point of projectile?	Horizontal only: $v = u\cos\theta$ (NOT zero)
Centripetal acceleration formula?	$a_c = \frac{v^2}{r} = \omega^2 r$ — toward centre
v-t graph: slope and area?	Slope = acceleration; Area = displacement
x-t graph: slope?	Slope = instantaneous velocity
Sign convention for free fall (upward +ve)?	g = −9.8 m/ $s^{2}$
Vector resolution formulas?	$A_x = A\cos\theta$ ; $A_y = A\sin\theta$
Scalar product vs vector product?	A·B = AB cosθ (scalar); A×B = AB sinθ (vector, ⊥ to both)

Summary: Kinematics covers motion without forces. For constant acceleration, use SUVAT equations (each omits one variable). Projectile motion separates horizontal (constant velocity) from vertical (uniform acceleration under g). Key traps: horizontal velocity is NOT zero at peak; complementary angles share range but differ in height (60° gives 3× the height of 30°). Circular motion keeps speed constant while continuously changing velocity direction. Always fix sign convention at the start and maintain it throughout.