14.7: Examples
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.
- What are the SI units of \(a\), \(b\), and \(c\)?
- 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\(^2\).
- What is the magnitude of the object's acceleration at \(t=0\)?
- What about at \(t=3.0\) s?