Question

Position of a particle is given by x = 5sin (t) cm, find its velocity at t = π/4, hence find acceleration at the same instant.​

Answer 1

Position function, X=Asin(πt+ϕ)......(1)

Velocity function, v=

dt

dX

=Aπcos(πt+ϕ)........(2)

Condition, (at t=0, velocity v=πcms

−1

andx=1cm )

From equation (1), 1=Asin(π×0+ϕ)......(3)

From equation (2), π=Aπcos(π×0+ϕ)........(4)

From (3) and (4)

tanϕ=1⇒ϕ=π/4

Put value in equation (3)

1=Asin(π×0+π/4)=Asin(π/4)

A=

2

cm

Hence, amplitude is

2

cm and phase is

4

π

Answered By

AMISHI