Question

if the velocity of a particle is uniform , then the path of the particle must be a ?​

Answer 1

Explanation:

A particle is moving with uniform velocity. Is it necessary to move with uniform speed? Is it necessary that it is moving along a straight line?

I teach my students when considering these questions to replace “velocity” with “speed and direction” (which defines velocity). So “uniform velocity” becomes “uniform speed and direction” and it is much more obvious that both speed and direction have to be uniform in this case.

Notice that reverse isn't true. Uniform speed does necessarily mean uniform “speed and direction”. So it is possible to have uniform speed but not have uniform velocity.

The answer is yes and yes.

Uniform velocity means unchanging velocity which in turn means unchanging speed and unchanging direction.

A particle can move with uniform velocity on a circular path, zigzags, etc.

Looks like the question has changed a bit.

So speed is the scalar/magnitude of velocity. In other words, if you have a velocity in the x and y direction according to a specified xy plane, your speed will be sqrt (x^2+y^2), where x and y are the velocities components.

Let's rotate the specified xy plane. Now of course, your velocity components in the x and y will change, however the magnitude of the speed will remain constant. So uniform velocity does indeed indicate uniform speed.

Necessary to move in a straight line? Nope. You can move with uniform velocity in a uniform circular motion.