Question

the position x of particle moving along x-axis varies with time t as x = Asin(kt) where A and k are positive constants. the acceleration a of particle varies with its position (x) as

1.a= Ax

2. a= -k2x

3 a = Akx

4 a = k2xA

Answer 1

V=dx/dt =Asin(kt) /dt= Acos(kt) k
a=dv/dt =Akcos(kt) /dt=Ak-sin(kt) k
=-Ak^2 sin(kt)

x=Asin(kt) so :- a=-kx