In one variable calculus, speed was the absolute value of the velocity. vi = initial velocity A particle starts from rest and has an acceleration function \(a(t)=\left(5-\left(10 \frac{1}{s}\right) t\right) \frac{m}{s^{2}}\). How far does the car travel in the 4 seconds it is accelerating? Working with a table of velocity values: To find out more or to change your preferences, see our cookie policy page. This calculus video tutorial explains the concepts behind position, velocity, acceleration, distance, and displacement, It shows you how to calculate the velocity function using derivatives and limits plus it contains plenty of notes, equations / formulas, examples, and particle motion practice problems for you to master the concept.Here is a list of topics:1. \], \[\textbf{v}_y(t) = v_1 \hat{\textbf{i}} + (v_2-9.8t) \hat{\textbf{j}}. \], Since the magnitude of our velocity is 100, we can say, \[\textbf{v}_y(0) = 100 \cos q \hat{\textbf{i}} + 100 \sin q \hat{\textbf{j}} . These deriv-atives can be viewed in four ways: physically, numerically, symbolically, and graphically. Get hundreds of video lessons that show how to graph parent functions and transformations. The axis is thus always labeled t (s). Legal. 2: Vector-Valued Functions and Motion in Space, { "2.1:_Vector_Valued_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.2:_Arc_Length_in_Space" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3:_Curvature_and_Normal_Vectors_of_a_Curve" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.4:_The_Unit_Tangent_and_the_Unit_Normal_Vectors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.5:_Velocity_and_Acceleration" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.6:_Tangential_and_Normal_Components_of_Acceleration" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.7:_Parametric_Surfaces" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "1:_Vector_Basics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2:_Vector-Valued_Functions_and_Motion_in_Space" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3:_Multiple_Integrals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4:_Integration_in_Vector_Fields" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "acceleration vector", "projectiles", "velocity", "speed", "showtoc:no" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FCalculus%2FSupplemental_Modules_(Calculus)%2FVector_Calculus%2F2%253A_Vector-Valued_Functions_and_Motion_in_Space%2F2.5%253A_Velocity_and_Acceleration, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), 2.4: The Unit Tangent and the Unit Normal Vectors, 2.6: Tangential and Normal Components of Acceleration.
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