A particle is moving in a circle

[mrknowknow]

A particle is moving in a circle of radius R in the xy plane. During the motion, neither the x- nor y-component of the particle's velocity exceeds v. Find the minimum possible time for the particle to complete one circle. (I.e., find the minimum possible period of revolution.)

Hint 1: I don't think it can be solved without Calculus.
Hint 2: Answer is in the form of an equation without any rounding of any numbers involved.


Considering I haven't taken Calculus yet I don't know the right way to approach this problem.

 

[HallsofIvy]

Since the problem says "minimum time" you can get at least an estimate without Calculus. The particle has maximum speed \sqrt{2} v so cannot go a distance 2\pi R is less than
\dfrac{2\pi R}{\sqrt{2} v}= \sqrt{2}\pi \dfrac{R}{v}.

 

[BruceW]

I think it means that the max possible x-component of velocity is v. But it is worded a bit vaguely.

edit: and a similar statement for y, separately.

edit again: never mind, I am being stupid. I thought there was a problem, but there is not.

edit number 3: yeah, my mistake was thinking the question gave the max values of components of velocity. But it does not. It gives upper bounds.

 

[DrClaude]

The particle has maximum speed \sqrt{2} v

Could you please explain your reasoning here?

 

[BruceW]

hehe, yeah, I thought the same thing initially.

 

[mrknowknow]

Well how would I solve the problem with Calculus?

 

[Saitama]

Not sure but if you consider the uniform circular motion, the conditions mentioned in the problem are satisfied.

Is it possible for you to post the answer?

 

[BruceW]

well calculus doesn't really help to get a better answer in this case. If they told you the velocity as a function of time, then you could use calculus. But they don't tell you that.

 

[BruceW]

even without assuming uniform motion, we can still get a 'minimum time'.

edit: (as Hallsofivy has done)

 

[mrknowknow]

Well My professor stated as a hint he doesn't think it could be solved without Calculus. Could he be wrong?

 

[BruceW]

the way you have described the problem, I don't think you need calculus. But you should make up your own mind. (Although I guess that might be tricky if you haven't been taught what calculus is).