Question

The acceleration of a particle, starting from rest, varies with time according to the relation a = -sω² sinωt The displacement of this particle at a time t will be
(a) s sin ω t
(b) s ω cos ω t
(c) s ω sin ω t
(d) $-\frac{1}{2}$(sω² sin ωt)t²

Answer 1

Answer:

A) s sin ω t

Explanation:

The acceleration of a particle starting from rest, varies with the time according to the relation A = sω² sinωt. The displacement of this particle at a time (t).

Since, a= dv/dt and v = ds/dt, thus if we double integrate a from 0 to t we will get a displacement.

Velocity from 0 to t = integral (-s ω^2sin(ωt) dt) = sw(cos ωt - 1)

Displacement from 0 to t = integral (velocity dt)

Thus, by using the Simple Harmonic Motion Aptitude, the formulas include x = S sin ωt and x = S cos ω.

= s.sin ω t