The position function x(t) of a particle moving along an x axis is x = 4.00 - 6.00t2, with x in meters and t in seconds. (a) at what time and (b) where does the particle (momentarily) stop? at what (c) negative time and (d) positive time does the particle pass through the origin?

The position function x(t) of a particle moving along an x axis is

a) The point at which particle stop, it's velocity = 0 m/s

  So dx/dt = 0

        0 = 0- 12t = -12t

  So when time t= 0, velocity = 0 m/s

    So the particle is starting from rest.

At t = 0 the particle is (momentarily) stop

b) When t = 0

SO at x = 4m the particle is (momentarily) stop

c) We have

   At origin x = 0

  Substituting

         t = 0.816 seconds or t = - 0.816 seconds

So when  t = 0.816 seconds and t = - 0.816 seconds, particle pass through the origin.

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