Question

Question #9c52c

Answer 1

Speed is taken to mean the magnitude of the velocity vector, `vec v`, and is thus a scalar quantity.

There are two types of measured speed: average speed and instantaneous speed. The latter is more commonly used, and generally involves more mathematics to calculate.

The average speed of a particle is its displacement `Deltax`. divided by the time interval, `Deltat`:

`v_("av") = (Deltax)/(Deltat)`

The instantaneous speed of a particle is defined as the limit of the average speed as the time interval `Deltat` approaches `0`. In terms of calculus, the instantaneous speed of the particle at any time `t` is the derivative of the particle's position with respect to time:

`v = (dx)/dt`, or `v = lim_(Deltatrarr0) (Deltax)/(Deltat)`

We don't need to include the displacement as a vector because speed itself is not a vector. The formula for instantaneous velocity does need the position vector, since velocity is a vector quantity.

If the components of the instantaneous velocity are known at a particular time, the magnitude of the velocity at that time is

`v = sqrt((v_x)^2 + (v_y)^2 + (v_z)^2)`

And the components of instantaneous velocity at any time is the time derivative of the coordinates at that time:

`v_x = dx/dt`, `v_y = dy/dt`, and `v_z = dz/dt`