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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.
Multiplying velocity (a vector) by time interval (a positive scalar) gives displacement since velocity is the instantaneous rate of change of position (displacement).
The velocity vector is tangent to the trajectory of the particle. Displacement [latex] \overset {\to } {r} (t) [/latex] can be written as a vector sum of the one-dimensional displacements [latex] \overset {\to } {x} (t),\overset {\to } {y} (t),\overset {\to } {z} (t) [/latex] along the x, y, and z directions.
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 \(\Delta \vec r \)).
We define angular velocity ω as the rate of change of angular displacement. In symbols, this is. ω = Δθ Δt, ω = Δ θ Δ t, where an angular rotation Δθ takes place in a time Δt. The greater the rotation angle in a given amount of time, the greater the angular velocity.
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.
