If a > 0, the particle is travelling at an increasing speed.
If v < 0, the particle is travelling towards the left (or towards the origin).
For questions like: for what values of x is f(x) is increasing, isn't it when f'(x) > 0 ?
look at v as f(x) and a as f'(x)
Since a [f'(x)] is > 0, v...