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Kinematics: Formula Cheat Sheet
Every key formula for Kinematics, with what it means and where it comes from.
| Formula | What it means | Topic |
|---|---|---|
| a = (v - u) / t | Acceleration equals change in velocity divided by time taken. | Acceleration Explained |
| a = Δv / t | Acceleration is the rate of change of velocity. | Acceleration Explained |
| v = g t | Velocity after t seconds of free fall from rest. | Free Fall and Gravity |
| s = 1/2 g t^2 | Distance fallen after t seconds from rest. | Free Fall and Gravity |
| v^2 = 2 g s | Velocity squared equals twice g times the distance fallen from rest. | Free Fall and Gravity |
| v_x = v cos θ | Horizontal component of the launch velocity. | Projectile Motion Basics |
| v_y = v sin θ | Vertical component of the launch velocity. | Projectile Motion Basics |
| range = v_x x time of flight | Horizontal distance equals horizontal velocity times time in the air. | Projectile Motion Basics |
| v_AB = v_A - v_B | Velocity of A relative to B equals A's velocity minus B's velocity. | Relative Velocity |
| drag = weight at terminal velocity | At terminal velocity, air resistance balances weight, so the net force is zero. | Terminal Velocity |
| v_t = sqrt(2 m g / (ρ A C_d)) | Terminal velocity depends on mass, air density, area and drag coefficient. | Terminal Velocity |
| v = u + a t | Final velocity equals initial velocity plus acceleration times time. | The SUVAT Equations of Motion |
| s = u t + 1/2 a t^2 | Displacement equals initial velocity times time plus half acceleration times time squared. | The SUVAT Equations of Motion |
| v^2 = u^2 + 2 a s | Final velocity squared equals initial velocity squared plus twice acceleration times displacement. | The SUVAT Equations of Motion |
| s = 1/2 (u + v) t | Displacement equals average velocity times time. | The SUVAT Equations of Motion |
| speed = distance / time | Average speed equals total distance travelled divided by time taken. | Velocity vs Speed: What's the Difference? |
| velocity = displacement / time | Average velocity equals displacement divided by time taken. | Velocity vs Speed: What's the Difference? |
| v = √(2 × g × h) | A falling object speeds up steadily under gravity, and its impact speed depends only on the height it fell from. | Free Fall Calculator |
| R = v₀² sin(2θ) ÷ g | A projectile's horizontal range depends on its launch speed, launch angle and gravity, with air resistance ignored. | Projectile Motion Calculator |
| v_rel = v₁ − v₂ | Relative velocity is the difference of the two velocities, and it can be negative when the second object is faster. | Relative Velocity Calculator |
| v = u + a × t | With constant acceleration, velocity grows steadily over time and displacement follows from the starting speed and acceleration. | SUVAT Motion Calculator |
| v_t = √(2 × m × g ÷ (ρ × A × C_d)) | A falling object stops speeding up when drag equals its weight, so heavier or sleeker objects fall faster at terminal speed. | Terminal Velocity Calculator |