Rate of Change of Radial Distance

Question

For the functions above representing the position of objects, compute the rate of change of the distance from the origin at $$t=1$$ (i.e. differentiate the radial distance, $$r(t) = \sqrt{x(t)^2+y(t)^2}$$). Rank the functions in order of increasing rate of change of distance.
 
| Function      | Parametric Representation                      |
|---------------|-----------------------------------------------|
| Function 1  | $$\langle t, t \rangle$$                        |
| Function 2  | $$\langle t, 0 \rangle$$                        |
| Function 3  | $$\langle \cos(t), \sin(t) \rangle$$            |
| Function 4  | $$\langle t^2, t^2 \rangle$$                     |

Accepted Answer

Function 3, Function 2, Function 1, Function 4

Answer

Function 3, Function 1, Function 2, Function 4

Answer

Function 2, Function 3, Function 1, Function 4

Answer

Function 1, Function 2, Function 3, Function 4

Function	Parametric Representation
Function 1	$$\langle t, t \rangle$$
Function 2	$$\langle t, 0 \rangle$$
Function 3	$$\langle \cos(t), \sin(t) \rangle$$
Function 4	$$\langle t^2, t^2 \rangle$$

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