Ranking Displacement of Vector Valued Functions

Question

For each vector–valued position function above, compute the displacement (i.e. the magnitude of $$\vec{r}(2)-\vec{r}(0)$$) over $$t \in [0,2]$$. Then rank the functions in order of increasing displacement.
 
| Function      | $$\vec{r}(t)$$                              | Interval: $t \in [0,2]$ |
|---------------|---------------------------------------------|----------------------------|
| 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 D, Function B, Function A, Function C

Answer

Function A, Function D, Function B, Function C

Answer

Function B, Function A, Function D, Function C

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

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