The displacement of a particle on a vibrating string is given by the equation s(t) = 15 + 1 4 sin(15πt) where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds.

Velocity = Ds(t)/Dt= 15πcos(15πt)

Step-by-step explanation:

The displacement is given by

s(t) = 15 + 1 4 sin(15πt)

The velocity of the particle on the vibrating string is the differential of the displacement.

The velocity will be equal to

Ds(t)/Dt

s(t) = 15 + 1 4 sin(15πt)

Ds(t)/Dt = D(15))Dt + D(sin(15πt))/Dt

Let sin(15πt) = sinu

Dsinu = cos u

U = 15πt

Du/Dt = 15π

Ds(t)/Dt= 0 + 15πcosu

Ds(t)/Dt= 15πcos(15πt)

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.