The function \small{s(t)} describes the position of a particle moving along a coordinate line,
where \small{s} is in feet and \small{t} is in seconds.
\small{s(t) = 6t^{2}-30t, \qquad t \ge 0}

(a) Find the velocity and acceleration functions.

(b) Over what interval is the particle moving in the positive direction?
Use ** inf ** to represent

Interval: |

(c) Over what interval is the particle moving in the negative direction?
Use ** inf ** to represent

Interval: |

(d) Over what interval is the particle speeding up? Slowing down?
Use ** inf ** to represent

Speeding up: | |

Slowing down: |

You can earn partial credit on this problem.