Calculus Based Physics Formulas: Mechanics

This is just a basic equation list, explanations can be found elsewhere. For the most part derivations are done for you, but it is beneficial to understand how an equation goes from one form to another.

One dimensional Equations of motion (along a single vector direction)
Velocity as a function of time : v_{xf} = v_{xi} + a_x t
Position as a function of time: x_f = x_i + v_{xi}t + \frac{1}{2} a_x t^2
Velocity as a function of position: v^2_{xf} = v^2_{xi} + 2a_x ( x_f &#8211; x_i)<br />

Projectile Motion
Horizontal motion
Velocity along x: v_{xi} = v_i cos(\theta)
Position from position as a function of time: x_f = v_i cos(\theta)t
Max Horizontal dist: R = v^2_i \frac{sin( 2 \theta_i)}{g}

Vertical Motion
Velocity along y:v_{yi} = v_i sin(\theta)
Position: from position as a function of timey_f = y_i + v_{yi}t &#8211; \frac{1}{2} g*t^2
Maximum Height: h_{max} = v^2_{i} \frac{sin(\theta_i)}{2g}

Circular Motion
Radial Acc: a_r = v^2_r = a cos( \theta)
Tan.

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