Ranking Displacement of Vector Valued Functions

Question

The table below defines four vector-valued position functions. For each function, the displacement over the interval $$t \in [0,2]$$ is the magnitude of the vector $$\vec{r}(2) - \vec{r}(0)$$. Which of the following correctly ranks the functions in order of increasing displacement?

| Function      | $$\vec{r}(t)$$                              |
|---------------|---------------------------------------------|
| Function A  | $$\langle t, t^2 \rangle$$                     |
| Function B  | $$\langle \cos(t), \sin(t) \rangle$$           |
| Function C  | $$\langle e^t, 0 \rangle$$                     |
| Function D  | $$\langle t, \ln(t+1) \rangle$$               |

Accepted Answer

Function B, Function D, Function A, Function C

Answer

Function B, Function A, Function D, Function C

Answer

Function D, Function B, Function A, Function C

Answer

Function A, Function D, Function B, Function C

Function	$\vec{r}(t)$
Function A	$\langle t, t^2 \rangle$
Function B	$\langle \cos(t), \sin(t) \rangle$
Function C	$\langle e^t, 0 \rangle$
Function D	$\langle t, \ln(t+1) \rangle$

Ranking Displacement of Vector Valued Functions

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