The displacement of a particle on a vibrating string is given by the equation s(t) = 15 + 1/2 sin(15πt)?
where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds.
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The velocity is simply the derivative of the position with respect to time, given by s(t) =15 + 1/2 sin(15*pi*t).
So ds/dt = [15*pi*sin(15*pi*t)]/2 and the velocity after t seconds would just be putting the value of t into the equation for ds/dt and getting some value.