What is constant velocity? This is in a question of moving charge.

[yungman]

This is in a question of finding retarded potential where the point charge is moving at constant velocity.

The book let the charge pass through the origin at t=0 so $$\vec w(t) = \vec v(t)$$ which I don't understand.

This might be a stupid question. velocity is a vector with amplitude and direction. So what is the meaning of constant velocity?

Of cause I know |v|= constant, but does constant velocity implies it travel in a straight line because traveling in a curve is not consider constant velocity?

 

[khemist]

A constant velocity is one where the derivative of that motion is zero. Traveling in a curve would require an acceleration (if moving in a circle, that acceleration is v^2/r), in which case the derivative of that velocity would not be zero.

Regarding the w(t) = v(t), I assuming they just want to set up a situation where there was no acceleration to get to the velocity v.

And I think it would be more correct to say the velocity vector has a magnitude, rather than an amplitude. Amplitudes are found in wave functions. However, to determine if something has a constant velocity, one would either need the velocity function, or would have to take measurements of the velocity at different times. If one took the tangential velocity of a particle moving about a circle, each vector measured would be "straight," in the sense it only has a direction and magnitude, but if I measured the velocity again at another point, it would not be pointing in the same direction.

One cannot find the derivative of a vector through normal differentiation, I believe you need the covariant derivative for that (dont quote me here ;)).

 

[tiny-tim]

Of cause I know |v|= constant, but does constant velocity implies it travel in a straight line because traveling in a curve is not consider constant velocity?

simple answer …

yes ​

 

[yungman]

Thanks all.