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Velocity and Acceleration — Operator Notation and Parametric Equations A free preview from The Ultimate Crash Course for STEM Majors by Jonathan David. Operator Notation $$ v=\frac{d}{dt}s(t)=\frac{ds}{dt}=s'(t)\equiv\dot{s} $$ Velocity in the x-Direction $$ v_x=\frac{d}{dt}x(t)=\frac{dx}{dt}=x'(t)\equiv\dot{x} $$ Velocity in the y-Direction $$ v_y=\frac{d}{dt}y(t)=\frac{dy}{dt}=y'(t)\equiv\dot{y} $$ Note: A graph described by $y=f(x)$ can also […]

Constant Acceleration — Kinematics, Integration, and Vector Notation A free preview from The Ultimate Crash Course for STEM Majors by Jonathan David. Note: The following formulas also apply in the $y$-direction when acceleration is constant. For vertical motion under gravity alone, the sign of the acceleration depends on your choice […]

Net Force and Newton’s Laws of Motion A free preview from The Ultimate Crash Course for STEM Majors by Jonathan David. Resultant Force $$ R_x = F_{x,1} + F_{x,2} + F_{x,3} + \cdots = \sum_i F_{x,i} $$ $$ R_y = F_{y,1} + F_{y,2} + F_{y,3} + \cdots = \sum_i F_{y,i} […]