Motion -- "find the greatest velocity" type questions - help needed (1 Viewer)

[cssftw]

Hi guys, here's the question I don't know how to do:

Q. A particle is attached to the end of an elastic string; it is projected vertically downwards from the point O with velocity sqrt(22) m/s, and has acceleration (10-2x) m/s/s after it has traveled x metres.

Find it's greatest velocity, and show that the motion is confined to a certain interval.

----

Can someone please explain to me how to do this? I mean with questions involving greatest displacement -- you just let v=0 right? So what's the deal with greatest velocity? Do you let acceleration = 0, or is there something else?

Help would be immensely appreciated! Thanks

 

[Aquawhite]

The greatest velocity does occur when the acceleration is zero. Have a go using that idea and report back to see how you've faired against the question.

 

[cssftw]

The greatest velocity does occur when the acceleration is zero.

Just to make sure, are you over 9000% that this is right? Could you explain why? Is it because greatest velocity is at a maxima, therefore acceleration = 0? But wouldn't that only work if acceleration and velocity are in erms of t (time)??

Also yeah, if it is right, then I got greatest velocity = 6(sqrt(2)) m/s

 

[hscishard]

Max velocity in shm is when x=0, i.e. centre of motion. This is when acceleration is 0. For that question you could integrate it to find v in terms of x.

What you said about maxima and acceleration = 0 isn't correct. Acceleration is max there