Show that a force that does no work must be a velocity dependent force.

Explanation

Let a force `vecF` does no work for the displacement `dvecl` while moving with velocity `vecv` for time `dt`.
Then work done, `dW=vecF.dvecl=0` or `vecF.vecvdt=0` or `vecF.vecv=0` or `Fvcostheta=0` or `theta=90^@`.
Therefore, for no work done, `vecF` must be velocity dependent if angle between `vecF` and `vecv` is `90^@`. If `vecv` changes its direction, then `vecF` should also change its direction so that angle between `vecF` and `vecv` is `90^@`. It is so when a charged particle is moving in a perpendicular uniform magnetic field.