Questions: r = [4.0 cm + (25 cm/s^2) t^2] i + (5.0 cm / s) t j t=0 r=4.0 cm t=2.0

Transcript text: $\begin{array}{l}\vec{r}=\left[4.0 \mathrm{~cm}+\left(\frac{25 \mathrm{~cm}}{\mathrm{~s}^{2}}\right) t^{2}\right] i+(5.0 \mathrm{~cm} / \mathrm{s}) \mathrm{t} \hat{j} \\ t=0 \quad \vec{r}=4.0 \mathrm{~cm} \\ t=2.0\end{array}$

Solution

Paso 1: Identificar la expresión de la posición en función del tiempo

La posición $\vec{r}$ está dada por: \[ \vec{r} = \left[4.0 \, \text{cm} + \left(\frac{25 \, \text{cm}}{\text{s}^2}\right) t^2 \right] \hat{i} + (5.0 \, \text{cm/s}) t \hat{j} \]

Paso 2: Evaluar la posición en $t = 0$

Para $t = 0$: \[ \vec{r}(0) = \left[4.0 \, \text{cm} + \left(\frac{25 \, \text{cm}}{\text{s}^2}\right) (0)^2 \right] \hat{i} + (5.0 \, \text{cm/s}) (0) \hat{j} = 4.0 \, \text{cm} \hat{i} \]

Paso 3: Evaluar la posición en $t = 2.0$ s

Para $t = 2.0$ s: \[ \vec{r}(2.0) = \left[4.0 \, \text{cm} + \left(\frac{25 \, \text{cm}}{\text{s}^2}\right) (2.0)^2 \right] \hat{i} + (5.0 \, \text{cm/s}) (2.0) \hat{j} \] \[ \vec{r}(2.0) = \left[4.0 \, \text{cm} + 100 \, \text{cm} \right] \hat{i} + 10.0 \, \text{cm} \hat{j} \] \[ \vec{r}(2.0) = 104.0 \, \text{cm} \hat{i} + 10.0 \, \text{cm} \hat{j} \]

Respuesta Final

$\boxed{\vec{r}(2.0) = 104.0 \, \text{cm} \hat{i} + 10.0 \, \text{cm} \hat{j}}$

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