A particle starts from origin at t=0 with velocity `5.0hati m//s` and move in x.y plane under action of a force which produces a constant acceleration of `(3.0hati+2.0hatj) m//s^(2)`. (a) What is the y-coordinate of the particle at the instant its x-ccordinate is 84 m? (b) What is the speed of the particle at this time?

Explanation

To solve the problem, we will break it down into two parts: (a) finding the y-coordinate when the x-coordinate is 84 m, and (b) calculating the speed of the particle at that time.

### Given Data:
- Initial velocity, \( \mathbf{u} = 5 \hat{i} \, \text{m/s} \)
- Acceleration, \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} \, \text{m/s}^2 \)
- Initial position, \( \mathbf{r_0} = 0 \hat{i} + 0 \hat{j} \, \text{m} \)

### Part (a): Finding the y-coordinate when x = 84 m
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