Question

why is repetitive motion required to measure time

Answer 1

The fundamental test of any clock is made when you build two of them and then intercompare them.  That's why we use atomic clocks; we can build hundreds of them and they agree remarkably well with each other.

Answer 2

Because repetitive motion is uniform and thus easily divisible.

Eg.
A car moves 20 km in every 10 min, how much time would it take to travel 120km?

Ans 1hr

Using unitary method , 10÷20=2km/per min.
120÷2=60(1hr has 60 mins.)
60÷60=1
Hence,proven