Only d ### Vector Motion in the x-y PlaneConsider an object moving in the x-y plane with a position vector represented by:\[ \vec{r} = (2t^3 - 5t) \hat{i} + (6 - t^4) \hat{j} \]where \( \vec{r} \) is in meters, and \( t \) is in seconds.To analyze the motion of the particle, solve the following:**a. Position vector at \( t = 0 \)s**\[ \vec{r}(t=0) = (2(0)^3 - 5(0)) \hat{i} + (6 - (0)^4) \hat{j} \]\[ \vec{r}(0) = 0 \hat{i} + 6 \hat{j} \]\[ \vec{r}(0) = 6 \hat{j} \text{ meters} \]**b. Position vector at \( t = 2 \)s**\[ \vec{r}(t=2) = (2(2)^3 - 5(2)) \hat{i} + (6 - (2)^4) \hat{j} \]\[ \vec{r}(2) = (2(8) - 10) \hat{i} + (6 - 16) \hat{j} \]\[ \vec{r}(2) = (16 - 10) \hat{i} + (-10) \hat{j} \]\[ \vec{r}(2) = 6 \hat{i} - 10 \hat{j} \text{ meters} \]**c. Displacement vector for this change in position**The displacement vector is the difference in the position vectors at \( t=2 \)s and \( t=0 \)s:\[ \Delta \vec{r} = \vec{r}(2) - \vec{r}(0) \]\[ \Delta \vec{r} = (6 \hat{i} - 10 \hat{j}) - (0 \hat{i} + 6 \hat{j}) \]\[ \Delta \vec{r} = 6 \hat{i} - 16 \hat{j} \text{ meters} \]**d. Average velocity during this motion**The

Name: Only d ### Vector Motion in the x-y PlaneConsider an object moving in
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: Only d ### Vector Motion in the x-y PlaneConsider an object moving in the x-y plane with a position vector represented by:\[ \vec{r} = (2t^3 - 5t) \hat{i} + (6 - t^4) \hat{j} \]where \( \vec{r} \) is in meters, and \( t \) is in seconds.To analyze th