Answer
$$26.14\frac{m}{s}$$
Work Step by Step
Before 2.4s:
$$ v_{me} = 110 \frac{km}{hr} · 1000 \frac{m}{km} ·\frac{1}{3600} \frac{hr}{sec} $$ $$= \frac{275}{9} \frac{m}{s}$$
$$ v_{police} = \frac{275}{9} - 2.5t $$
$$ d_{police} = \frac{275}{9}t - \frac{1}{2} · 5 · t^{2}$$
$$ d_{me} = \frac{275}{9} · t = \frac{275}{9} · 2.4 = \frac{220}{3} m$$
After 2.4s :
$$ d_{me} = \frac{275}{9} (t - \frac{12}{5}) - \frac{5}{2} (t - \frac{12}{5})^{2} +\frac{220}{3} $$
$$ d_{me} =- \frac{5}{2}t^{2} + \frac{383}{9}t - \frac{72}{5}$$
$$ v_{me} =d_{me} \frac{d}{dt} = -5t + \frac{383}{9}$$
Equating $d_{me}$ and $d_{police}$:
$$- \frac{5}{2}t^{2} + \frac{383}{9}t - \frac{72}{5} = \frac{275}{9}t - \frac{5}{2} t^{2}$$
$$ t =\frac{197}{60} \space s$$
Solving for velocity:
$$ v_{me}(\frac{197}{60}) = -5(\frac{197}{60})+\frac{383}{9} = \frac{941}{36} = 26.14 \space \frac{m}{s}$$
