When does the policeman catch the thief 100 meters ahead?

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aprao
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Hai Expert
COuld you please explain to me how to solve the following problems?

Question:
A Thief sees a policeman 100 Metre ahead of him. He Immediately turns back and starts running at 6Kmph. The Policeman chases him at a speed of 8Kmph. After What time does the policeman catch up with the thief ?


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aprao
 

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Version 1:
1) Let your origin coincide with your police-man's initial position
How can we write the police-man's subsequent position (measured relative, that is, to the origin) as a function of time?
2) Measured from the policeman's initial position, the thief's initial position is 100.
How can we write the thief's subsequent position (measured relative, that is, to the origin) as a function of time?

3) Since at the time when the policeman catches up with the thief, their positions is the same, you may find an equation for the time by equating their position functions at that time.

Version 2:
Compute the relative velocity the policeman has to the thief.
How long would it take a person runnning with this relative velocity to travel 100 meters?

I strongly suggest you work out the time by both versions, and verify that both versions predict the same time.
This will help you enhancing your understanding of the maths&physics involved.