A particle motion problem in the x-y plane with constant acceleration

[haruspex]

@haruspex what path does the particle take in xy plane? Can you draw?

The acceleration is constant. What familiar path results from constant acceleration?

 

[rudransh verma]

The acceleration is constant. What familiar path results from constant acceleration?

Since the position vector is quadratic so it will be a parabolic path.
Idk about constant acceleration path.

 

[haruspex]

Idk about constant acceleration path.

What planet are you on?

 

[rudransh verma]

What planet are you on?

Not linear

 

[jbriggs444]

Since the position vector is quadratic so it will be a parabolic path.
Idk about constant acceleration path.

In this case: is the position vector quadratic?
In this case: is acceleration constant?
In the general case: if acceleration is constant, will the position vector be quadratic?

If a ball is thrown in vacuum with constant gravity, its trajectory is parabolic, yes?
If you rotate the coordinate system, is its trajectory still parabolic?

 

[rudransh verma]

Sure.
To get the scalar eqns from the vector, take the dot product with, respectively, $\hat x, \hat y$.
Conversely, multiply the scalar equns by respectively, $\hat x, \hat y$, and add them to produce the vector equn.

Still working on latex

 

[haruspex]

Still working on latex

Yes.