Equation of Motion in different co-ordinate space Suppose I have a particle in 2D cartesian space. It has an equation of motion which is straight line.
If I change the co-ordinate (Say Polar co-ordinate), will the equation of motion will be straight line or not?
If No: What is intuition behind this?
 A: The physics does not depend on the choice of coordinates: a straight line is a straight line.  Of course the actual description of a straight line (i.e. the actual equation to be satisfied by the points on a straight line) is not the same in different coordinate system (see for instance this webpage).
The form of the equation of motion will also change, but the resulting motion will still be a straight line, just expressed in a somewhat clumsy coordinate system to see the simplicity of the resulting motion.
A: I think @ZeroTheHero gave a good answer to the question but I believe your confusion is rooted from another point of view. When a coordinate change as cartesian to polar is done what you do is simply name the same object from a different perspective and you get the same equation with different naming but here comes the confusion assume you have an observer in Cartesian coordinates and if observer draws a line then this line has some constant relation between ratio of x and y values where simply y is function of x and lets consider the case where y=2 and x is independent variable or vice versa we simply get a straight line and we observe this result as an observer who only understand cartesian unit vectors but when it comes to the polar coordinates then x,y changes to r and $\theta$ and as it's done in cartesian if assuming r is constant and $\theta$ is independent variable then you get a something who can observe with polar unit vectors but a cartesian observer will see the result as a circle and if as it's done on cartesian system we name the polar observer's result as a line then things will get weird and have no meaning physically but as a thought you can say it as a line but in your question your change of coordinates merely, a path that is in cartesian a line is named in polar coordinates and resulted in a line but this is because you simply try to draw the same path with different unit vectors so get the same thing and when cartesian equation's plot and polar's are compared they will match. From the physical perspective @ZeroTheHero explains the detail very well.
