Error Analysis — Common Kinematics Mistakes — Notes

Mistake	Why It's Wrong	Correction
Setting velocity at highest point = 0	Only vertical component is zero; horizontal component $u\cos\theta$ persists	At peak: $v = u\cos\theta$ (minimum speed, not zero)
Using g = +9.8 when upward is positive	Sign convention violated; g acts downward	If upward +ve, g = −9.8 m/ $s^{2}$ ; if downward +ve, g = +9.8 m/ $s^{2}$
Confusing distance with displacement	Path of 10 m in a semicircle has displacement = diameter, not 10 m	Displacement = straight-line separation between start and end
Applying SUVAT when acceleration is not constant	SUVAT derived assuming a = const; invalid for variable acceleration	Use integration: $v = \int a\,dt$ or graphical area method
Range of 30° > range of 60° (same u)	Both are complementary; ranges are equal	$R_{30} = R_{60} = \frac{u^2\sin 60°}{g}$
s_n formula gives total displacement	$s_n$ is displacement DURING the nth second only	Total displacement after n seconds = $un + \frac{1}{2}an^2$
Forgetting $\frac{1}{2}$ in $s = ut + \frac{1}{2}at^2$	Writing $s = ut + at^2$ leads to factor-of-2 error	Always write $\frac{1}{2}at^2$ ; derive from $s =$ area under v-t triangle
Equating angular velocity (rad/s) to linear velocity (m/s)	Different dimensions: $[\omega] = T^{-1}$ vs $[v] = LT^{-1}$	Use $v = \omega r$ to convert between them
Area under x-t graph = displacement	Area under x-t graph has dimension $[L][T]$ — not displacement	Area under v-t graph = displacement; slope of x-t graph = velocity
Using sin(2θ) = 2sinθ	Incorrect trig identity	$\sin 2\theta = 2\sin\theta\cos\theta$ ; for θ = 45°: sin 90° = 1