Help with trigonmetric function question..

[maccaman]

This is a problem solving one, i just dont know where to start it though

The speed of a particle in an alternating current is given by the equation:

v = 3 cos t/3, where v is in cm/s and t is in seconds.

The particle's movement begins at its point of equilibrium.
How soon after the start would the particle first reach a displacement of
-4.5cm?

[Integral]

You are given an expression for the velocity, you need to find the displacement.

v = \frac {dx} {dt}

so

\frac {dx} {dt} = 3 cos (\frac t 3)

\int dx = \int 3 cos (\frac t 3) dt

You should now be able to find an expression for the displacement as a function of time. You will need to find the time that satifies your conditions.