Ranking Vector Function Acceleration Magnitudes

Question

Consider the four vector-valued functions, $$\vec{r}(t) = \langle x(t), y(t) \rangle$$, shown in the table. Rank the functions in order of increasing magnitude of their acceleration vector, $$|\vec{a}(t)| = \sqrt{(x''(t))^2+(y''(t))^2}$$. The acceleration should be evaluated at $$t=1$$ for Functions 1, 3, and 4, and at $$t=\frac{\pi}{6}$$ for Function 2.

| Function      | $$\vec{r}(t)$$                               |
|---------------|----------------------------------------------|
| Function 1    | $$\langle t, t^2 \rangle$$                    |
| Function 2    | $$\langle \cos(t), \sin(t) \rangle$$          |
| Function 3    | $$\langle e^t, e^t \rangle$$                   |
| Function 4    | $$\langle t^2, \ln(t+1) \rangle$$             |

Accepted Answer

Function 2, Function 1, Function 4, Function 3

Answer

Function 1, Function 2, Function 4, Function 3

Answer

Function 2, Function 4, Function 1, Function 3

Answer

Function 1, Function 4, Function 2, Function 3

Function	$\vec{r}(t)$
Function 1	$\langle t, t^2 \rangle$
Function 2	$\langle \cos(t), \sin(t) \rangle$
Function 3	$\langle e^t, e^t \rangle$
Function 4	$\langle t^2, \ln(t+1) \rangle$

Ranking Vector Function Acceleration Magnitudes

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