Sita is driving along a staight highway in her car. At time `t=0`, when Sita is moving at `10ms^-1` in the positive x-direction, she passes a signpost at `x=50m`. Here acceleration is a function of time:
`a=2.0ms^-2-(1/10ms^-3)t`
a. Derive expressions for her velocity and position as functions of time.
b. At what time is her velocity greatest?
c. What is the maximum velocity?
d. Where is the car when it reaches the maximum velocity?

Explanation

To solve the problem, we need to derive expressions for Sita's velocity and position as functions of time, determine when her velocity is greatest, find the maximum velocity, and finally, calculate her position when she reaches that maximum velocity.

### Step-by-Step Solution

**Given:**
- Initial velocity, \( v_0 = 10 \, \text{m/s} \)
- Initial position, \( x_0 = 50 \, \text{m} \)
- Acceleration as a function of time, \( a(t) = 2.0 \, \text{m/s}^2 - \frac{1}{10} \, \text{m/s}^3 \cdot t \)
...