Question

The displacement X as a function of time t is given as X = a sinꙍt .The acceleration of the particle is:

Answer 1

Answer:

A = - a sinꙍt

Explanation:

Velocity = d(X)/dt

Acceleration = d(V)/dt

let us assume Velocity be V and Acceleration be A

X = a sinꙍt

V = a cosꙍt

A = - a sinꙍt

Answer 2

Explanation:

differentiate both sides with respect to time

dx/dt = a cos wt {d(wt)/dt}

[since w is constant and dt/dt =1]

dx/dt = a w coswt

dx/dt = velocity v

v = a w coswt

similarly again differentiate both sides with respect to time

dv/dt = -a w^2 sinwt

dv/dt = acceleration

• acceleration of the particle is -aw^2sinwt