A particle of mass m kept at the origin is subjected to a froce `vecF=(pt-qx)hati` where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t=0 with zero initial velocity. If p and q are positive constants, then:

Options

A. The acceleration of the particle will continously keep on increasing with time.
B. Particle will execute simple harmonic motion.
C. The force on the particle will have no upper limit.
D. The acceleration of particle will very sinusoidally with time.

Explanation

`F=pt-qx`
`rArra=(1)/(m)(pt-qx) rArr (da)/(dt)=([p-qv])/(m)`
`rArr(d^(2)a)/(dt^(2))=-(q)/(m)a[=-omega^(2)a] rArromega=sqrt((q)/(m))`