Equations of Motion

Projectile Motion

$T = \frac{2u\sin\theta}{g} \qquad H = \frac{u^2\sin^2\theta}{2g} \qquad R = \frac{u^2\sin 2\theta}{g}$

• Max range at θ = 45°: $R_{max} = \frac{u^2}{g}$
• Complementary angles → same R, $\frac{H_2}{H_1} = \tan^2\theta$
• At peak: v = u cosθ (not zero); $v_y = 0$

Circular Motion

$\omega = \frac{v}{r} \quad [\text{rad/s}] \qquad a_c = \frac{v^2}{r} = \omega^2 r \quad [\text{m/s}^2, \text{ toward centre}]$

Graph Rules

• x-t slope = velocity | v-t slope = acceleration | v-t area = displacement

Critical Values

• $g = 9.8 \approx 10$ m/$s^{2}$ | $\sin 30° = 0.5$, $\cos 30° = 0.866$, $\sin 45° = 0.707$, $\sin 60° = 0.866$

Sign Convention

• Fix one direction as positive; maintain throughout entire problem
• Free fall, upward positive: g = −9.8 m/$s^{2}$