A particle executing SHM according to the equation `x=5cos(2pit+(pi)/(4))` in SI units. The displacement and acceleration of the particle at t=1.5 s is

Options

A. `-3.0m,100ms^(-2)`
B. `+2.54m,200ms^(-2)`
C. `-3.54m,140ms^(-2)`
D. `+3.55m,120ms^(-2)`

Answer

C

Explanation

The given equation of simple harmonic motion is
`x(t)=5cos(2pit+(pi)/(4))` ltbr Compare the given equation with standard equation of SHM
`x(t)=Acos(omegat+phi)`
we get, `omega=2pis^(-1)`
at t=1.5s
Displacement, `x(t)=5cos(2pixx1.5+(pi)/(4))`
`=5cos(3pi+(pi)/(4))=-5cos((pi)/(4))`
`=-5xx0.707m=-3.54m`
acceleration, `a=-omega^(2)xx`displacement
`=-(2pis^(-1))^(2)xx(-3.54m)=140ms^(-2)`