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University Physics Volume 1

Key Equations

University Physics Volume 1Key Equations

Key Equations

Displacement

Δ x = x_{f} - x_{i}

Total displacement

Δ x_{Total} = \sum Δ x_{i}

Average velocity

\overset{–}{v} = \frac{Δ x}{Δ t} = \frac{x_{2} - x_{1}}{t_{2} - t_{1}}

Instantaneous velocity

v (t) = \frac{d x (t)}{d t}

Average speed

Average speed = \overset{–}{s} = \frac{Total distance}{Elapsed time}

Instantaneous speed

Instantaneous speed = | v (t) |

Average acceleration

\overset{–}{a} = \frac{Δ v}{Δ t} = \frac{v_{f} - v_{0}}{t_{f} - t_{0}}

Instantaneous acceleration

a (t) = \frac{d v (t)}{d t}

Position from average velocity

x = x_{0} + \overset{–}{v} t

Average velocity (for constant acceleration)

\overset{–}{v} = \frac{v_{0} + v}{2}

Velocity from acceleration

v = v_{0} + a t (constant a)

Position from velocity and acceleration

x = x_{0} + v_{0} t + \frac{1}{2} a t^{2} (constant a)

Velocity from distance

v^{2} = v_{0}^{2} + 2 a (x - x_{0}) (constant a)

Velocity of free fall

v = v_{0} - g t (positive upward)

Height of free fall

y = y_{0} + v_{0} t - \frac{1}{2} g t^{2}

Velocity of free fall from height

v^{2} = v_{0}^{2} - 2 g (y - y_{0})

Velocity from acceleration

v (t) = \int a (t) d t + C_{1}

Position from velocity

x (t) = \int v (t) d t + C_{2}

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- Authors: William Moebs, Samuel J. Ling, Jeff Sanny
- Publisher/website: OpenStax
- Book title: University Physics Volume 1
- Publication date: Sep 19, 2016
- Location: Houston, Texas
- Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
- Section URL: https://openstax.org/books/university-physics-volume-1/pages/3-key-equations

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