Answer:
3 seconds
Explanation:
We can give an expression for the position of both the thief and of the police officer at time t.
The position of the thief at time t is given by
[tex]x_t = 9 + 5t[/tex]
where 9 is its initial position in m and 5 is its speed in m/s.
Instead, the position of the police officer at time t is given by
[tex]x_o = 0+8t[/tex]
where 0 is its initial position in m and 8 is its speed in m/s.
The police officer will catch the thief when their position will be equal, so
[tex]x_t = x_o[/tex]
By solving,
[tex]9+5t=8t\\3t=9\\t=3 s[/tex]
