Radius Vector Homework: Find Velocity, Acceleration, Time, & Distance

[phisics99]

Homework Statement

A radius vector of a particle varies with time t as r=at(1-\alphat) where "a" is a constant vector \alpha is a positive factor.
Find:
a) velocity "v" and the acceleration \omega as function of time;
b) the time interval \Deltat taken by the particle to return to the initial points and the distance "s" covered during this time.

I have solved a) and have problem with b)

Homework Equations

r=at(1-\alphat)
v=a(1-2\alphat)
\omega=-2\alpha

The Attempt at a Solution

To find time I should divide r/v? I don't understand that. The result is: t=1/\alpha.
Now how find distance? Substitute founded time to equation as r?
Looking for some help, my phisical english isn't so good , because come from Poland. Thx

 

[tiny-tim]

Welcome to PF!

Hi phisics99! Welcome to PF!

(have an alpha: α and an omega: ω )

A radius vector of a particle varies with time t as r=at(1-\alphat) where "a" is a constant vector \alpha is a positive factor.
Find:
a) velocity "v" and the acceleration \omega as function of time;
b) the time interval \Deltat taken by the particle to return to the initial points and the distance "s" covered during this time.
…
To find time I should divide r/v? I don't understand that. The result is: t=1/\alpha.
Now how find distance? Substitute founded time to equation as r?

(btw, your ω is missing an α )

To find time, just use the original equation, r = at(1 - αt) …

r = 0 at t = 0 and at t = … ?

(and then use one of the standard constant acceleration equations to get distance)