Question

What is the difference between instantaneous velocity and speed?

Answer 1

Velocity is a vector and speed is a magnitude.

Recall that a vector has direction and magnitude. Speed is simply the magnitude. Direction can be as simple as positive and negative. Magnitude is always positive.

In the case of positive/negative direction (1D), we can use the absolute value, `|v|`.

However, if the vector is 2D, 3D, or higher, you must use the Euclidean norm: `||v||`. For 2D, this is
`||v||=sqrt(v_x^2+v_y^2)`
And as you can guess, 3D is:
`||v||=sqrt(v_x^2+v_y^2+v_z^2)`