Linear Motion - Particle Displacement

[IntegrateMe]

The function v(t) = 9 - t² is the velocity in m/sec for a particle moving along the x-axis, where t is measured in seconds (t is greater than or equal to 0). Use analytic methods to solve:

(a) When the particle is moving to the right, to the left, and stopped.
(b) The particles displacement for 0 <= t <= 6 (<= means "less than or equal to")
(c) The total distance the particle traveled for 0 <= t <= 6

I'm going to be honest, i have no idea how to even start on the problem. Any help would be greatly appreciated.

 

[rl.bhat]

v(t) = dx/dt = 9 - t^2.
So dx = (9-t^2)*dt.
Find the integration and equate it to zero. You will get t for which the displacement is zero.