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14.7: Examples

  • Page ID
    63248
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    Whiteboard Problem \(\PageIndex{1}\): A Pair of Vector Problems

    Position to Velocity:

    An object's position as a function of time is given by
          \[\vec{r}(t)=\frac{c}{bt+1}\hat{x}+cbt\hat{y}+at^2\hat{z},\]
    where \(a\), \(b\), and \(c\) are constants.

    1. What are the SI units of \(a\), \(b\), and \(c\)?
    2. Find an expression of the object's speed as a function of time.

    Velocity to Acceleration:

    An object's velocity as a function of time has components

    \[v_x(t)=bt^2+c\]
    \[v_y(t)=qt\]
    \[v_z(t)=0,\]
    where \(b=10\) m/s\(^3\), \(c=5\) m/s, and \(q=-2.0\) m/s\(^2\).

    1. What is the magnitude of the object's acceleration at \(t=0\)?
    2. What about at \(t=3.0\) s?

    14.7: Examples is shared under a CC BY-SA license and was authored, remixed, and/or curated by Christopher Duston, Merrimack College.

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