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Calculate the velocity vector given the position vector as a function of time. Calculate the average velocity in multiple dimensions. Displacement and velocity in two or three dimensions are straightforward extensions of the one-dimensional definitions.
Calculate position vectors in a multidimensional displacement problem. Solve for the displacement in two or three dimensions. Calculate the velocity vector given the position vector as a function of time.
The displacement vector [latex] \text{Δ}\overset{\to }{r} [/latex] gives the shortest distance between any two points on the trajectory of a particle in two or three dimensions. Instantaneous velocity gives the speed and direction of a particle at a specific time on its trajectory in two or three dimensions, and is a vector in two and three ...
In two (or more) dimensions, you define the average velocity vector as a vector \(\vec v_{av}\) whose components are \(v_{av,x} = \Delta x/ \Delta t\), \(v_{av,y} = \Delta y/ \Delta t\), and so on (where \(\Delta x\), \(\Delta y\),... are the corresponding components of the displacement vector \(\Delta \vec r \)).
Define position, displacement, and distance traveled. Calculate the total displacement given the position as a function of time. Determine the total distance traveled. Calculate the average velocity given the displacement and elapsed time.
The displacement vector gives the shortest distance between any two points on the trajectory of a particle in two or three dimensions. Instantaneous velocity gives the speed and direction of a particle at a specific time on its trajectory in two or three dimensions, and is a vector in two and three dimensions.
The velocity of an object is its speed in a given direction. The displacement of an object is the distance it travels in a particular direction. Displacement and velocity are both vector quantities. Velocity has a positive value in one direction and negative value in the opposite direction.
