The equation of a progressive wave travelling along a string is given by
`y=10 sinpi(0.01x-2.00t)`
where x and y are in centimetres and t in seconds. Find the (a) velocity of a particle at x=2 m and `t=5//6` s. (b) acceleration of a particle at x=1 m and `t=1//4` s. also find the velocity amplitude and acceleration amplitude for the wave.

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as specified in the question.

### Given:
The wave equation is:
\[ y = 10 \sin(\pi(0.01x - 2t)) \]
where \( x \) and \( y \) are in centimeters and \( t \) is in seconds.

### Part (a): Find the velocity of a particle at \( x = 2 \, \text{m} \) and \( t = \frac{5}{6} \, \text{s} \).
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