2d Motion, calculating time when v=0 from position vector

[bearandmoose]

Homework Statement

The position vector of a particle is given by r= ihat(2t^3-21t^2+60t+10) +jhat(3/2)(t^2-10t+9)
At what time, if any, is the velocity of the particle zero (ie what time is the particle instantaneously at rest)

Homework Equations

The Attempt at a Solution

Finding the velocity vector is simple, just taking the derivative of position
However, when I set that to 0 I have the ihat and the jhat and I don't know how to combine them to solve for the time. Is this even the right step?

If I take
v= (6t^2-42t+60)ihat+(3t^2-15)jhat
and set that to 0
how do I account for the vx and vy when setting that to 0?
Do I set vx and vy to 0 separately?

I'm really confused.

Thanks.

 

[SammyS]

In order for v to be zero, both components must be zero. (at the same time, of course)