# Difference between revisions of "009A Sample Midterm 1, Problem 5"

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(Created page with "<span class="exam">The displacement from equilibrium of an object in harmonic motion on the end of a spring is: ::<span class="exam"><math>y=\frac{1}{3}\cos(12t)-\frac{1}{4}\...") |
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− | |What is the relationship between position <math style="vertical-align: -5px">s(t)</math> and velocity <math style="vertical-align: -5px">v(t)</math> of an object? | + | |What is the relationship between the position <math style="vertical-align: -5px">s(t)</math> and the velocity <math style="vertical-align: -5px">v(t)</math> of an object? |

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| <math>v(t)=s'(t)</math> | | <math>v(t)=s'(t)</math> |

## Revision as of 19:24, 13 April 2017

The displacement from equilibrium of an object in harmonic motion on the end of a spring is:

where is measured in feet and is the time in seconds.

Determine the position and velocity of the object when

Foundations: |
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What is the relationship between the position and the velocity of an object? |

**Solution:**

Step 1: |
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To find the position of the object at |

we need to plug into the equation |

Thus, we have |

Step 2: |
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Now, to find the velocity function, we need to take the derivative of the position function. |

Thus, we have |

Therefore, the velocity of the object at time is |

Final Answer: |
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position is |

velocity is |