Rate of Change of Radial Distance

Question

The table provides four vector-valued functions, each representing the position of an object at time $$t$$. The distance of the object from the origin is given by the function $$r(t) = \sqrt{x(t)^2 + y(t)^2}$$. Rank the four functions in increasing order of the rate of change of their distance from the origin at $$t=1$$.

| 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 2, Function 3, Function 1, Function 4

Answer

Function 3, Function 1, Function 2, 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	$\langle t^2, t^2 \rangle$

Rate of Change of Radial Distance

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