Kinematics Cheatsheet

Cheat Codes & Shortcuts

• Displacement: \( s = vt \) (constant velocity)
• Average Velocity: \( v_{avg} = \frac{\Delta s}{\Delta t} \)
• Acceleration: \( a = \frac{\Delta v}{\Delta t} \)
• First SUVAT Eq: \( v = u + at \)
• Second SUVAT Eq: \( s = ut + \frac{1}{2} a t^2 \)
• Third SUVAT Eq: \( v^2 = u^2 + 2a s \)
• Free Fall (no air): \( a = g = 9.8\,\text{m/s}^2 \)
• Projectile Range: \( R = \frac{u^2 \sin 2\theta}{g} \)
• Max Height (projectile): \( H_{max} = \frac{u^2 \sin^2 \theta}{2g} \)
• Time of Flight: \( T = \frac{2u \sin \theta}{g} \)

Quick Reference Table

Concept	Equation / Formula	Example / Notes
Displacement	\( s = vt \)	10s at 5m/s → 50m
SUVAT 1	\( v = u + at \)	u=0, a=2, t=3 → v=6m/s
SUVAT 2	\( s = ut + \frac{1}{2} at^2 \)	u=2, a=1, t=4 → s=12m
SUVAT 3	\( v^2 = u^2 + 2as \)	u=3, a=2, s=4 → v=5m/s
Projectile Range	\( R = \frac{u^2 \sin 2\theta}{g} \)	u=10, θ=45° → R ≈ 10.2m
Max Height	\( H_{max} = \frac{u^2 \sin^2 \theta}{2g} \)	u=10, θ=60° → H ≈ 3.8m

Advice

Kinematics Quick Tips

• Constant velocity: Use \( s = vt \).
• Uniform acceleration: SUVAT equations are valid.
• Free fall: Acceleration is always \( g = 9.8\,\text{m/s}^2 \).
• Projectile motion: Resolve initial velocity into horizontal and vertical components.
• Time symmetry: Upward time equals downward time in projectiles (ignore air resistance).

Kinematics Speed Quiz

Test your speed with 5 kinematics questions! You have 30 seconds per question.