A particle starts from the origin at ` t=0` with a velocity of ` 10.0 hat j m//s` and moves in the x-y plane with a constant acceleration of ` ( 8.0 hat i + 2. 0 hat j ) ms^(-2)` . (a) At what time is the x-coordinate of the particle ` 16 m` ? What is the y-coordinate of the particle at that time ? (b) What is the speed of the particle at that time ?

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as per the question.

### Part (a): Finding the time when the x-coordinate is 16 m and the corresponding y-coordinate.

1. **Identify the initial conditions:**
- Initial position: \( \vec{r_0} = 0 \hat{i} + 0 \hat{j} \) (origin)
- Initial velocity: \( \vec{v_0} = 0 \hat{i} + 10.0 \hat{j} \, \text{m/s} \)
- Acceleration: \( \vec{a} = 8.0 \hat{i} + 2.0 \hat{j} \, \text{m/s}^2 \)
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