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# Math III

### Particle Motion & Related Rates

Question | Answer |
---|---|

How to find position formula | should be given to you; x(t) |

Find velocity at time t. | Find velocity formula; find derivative of x(t) |

When is the particle at rest? | set v(t)=0; solve for t |

When is the particle moving in a positive direction? | set v(t)>0; use zeros on ↔ to find when values are + |

Find acceleration at time t. | Find derivative of v(t) or find x''(t) |

initial velocity of the particle | find v(0) |

Is the particle accel. or decel. at t=__ sec? | Find accel. of whatever time given; determine by > or < |

Accelerating or decelerating ? a(3)>0 | accelerating |

Accelerating or decelerating? a(3)<0 | decelerating |

In what direction is the particle moving at t=__sec? | Find v of whatever time is given; determine by > or < |

In what direction is the particle moving if v is +? | ↑ or → |

In what direction is the particle moving if v is -? | ↓ or ← |

When is the particle slowing down? | when a(t) & v(t) have opposite signs on ↔ |

when given dy/dx which variable will have a derivative w/o needing the notation? | x |

What is the unit for volume using ft? | ft^3 |

What is the unit for area using ft? | ft^2 |

What is the unit for anything else using ft? | ft |

What does "how fast" mean for a related rates problem? | find the rate |

When doing any related rates problem what will always be at the bottom (i.g. dy/dx)? | dt |

When doing any related rates problem what will always be at the top (i.g. dy/dx)? | whatever you're looking for |

*don't forget to study/practice graph & chart problems!* | N/A |

When is the particle speeding up? | when a(t) & v(t) have the same sign on ↔ |

Give all the times when the object is moving → | set v(t)>0; use zeros on ↔ to find when values are + |

another way to ask when is the particle moving in a positive direction | Give all the times when the object is moving → |

Find the times when the particle changes direction | Give intervals where v(t) & a(t) have the same sign w/o including - numbers |

When writing time intervals what type of numbers should you NEVER include? | negative numbers |

Why should you never include negative numbers when talking about time? | time is never negative |

area of square formula | A=s^2 |

area of circle formula | A=pi*r^2 |

volume of cube formula | V=s^3 |