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 step by step, we will derive expressions for velocity and position, determine the time at which the velocity is greatest, find the maximum velocity, and finally calculate the position when the maximum velocity is reached.

### 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, \( a(t) = 2.0 \, \text{m/s}^2 - \frac{1}{10} \, \text{m/s}^3 \cdot t \)
...