1.Bird distance between two approaching trains.
Sol: Relative speed of trains = $20 + 30 = 50 \text{ km/h}$.
Time taken for collision = $\frac{100 \text{ km}}{50 \text{ km/h}} = 2 \text{ hours}$.
Distance flown by bird = $\text{Bird's speed} \times \text{Time} = 60 \times 2 = 120 \text{ km}$.
2.Acceleration & displacement for $v^2 = 100 - 4x$.
Sol: Differentiating wrt $x$: $2v \frac{dv}{dx} = -4 \implies v \frac{dv}{dx} = -2 \implies a = -2 \text{ m/s}^2$.
When $v = 0$: $0 = 100 - 4x \implies 4x = 100 \implies x = 25 \text{ m}$.
