How Do You Analyze Particle Motion Given a Position Function?

[spin360]

Homework Statement

The position of a particle is given by the function x = ( 8t^3 - 3t^2 + 5) m, where t is in s.
(a) At what time or times does vx = 0 m/s?

(b) What are the particle's position and acceleration at t1?

What are the particle's position and acceleration at t2?

Homework Equations

v1 = v0 + at
x1 = x0 + v0 + (1/2)at^2
vx = dx/dt
a = dv/dt

The Attempt at a Solution

Quite honestly, I'm not sure where to begin with this problem. If someone could help me to start it that would be greatly appreciated, thanks!

 

[hage567]

You know that v = dx/dt, and a = dv/dt. So for starters, take the derivatives.

 

[mjsd]

1.
v1 = v0 + at
x1 = x0 + v0 + (1/2)at^2

these are equation for constant acceleration. for your case acceleration is time dependent so can't use these