Apolice officer is chasing a purse-snatcher down a street. the thief
starts 9 meters ahead of the officer and can run 20 meters in 4 second
(5 m/s). the police officer can run 32 meters in 4 seconds (8 m/s). how long will it take the officer to catch the thief?

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

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

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

By solving,

its a 5.5 n

glad that

it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going   so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me