I just again need verification on the answers to some questions. Thanks
A particle is moving such that its displacement after t seconds is given by x=3sin2t metres.
a)Find the initial velocity and acceleration
b)Find the maximum displacement
c)Find the times when the particle will be at rest
d)Prove that the acceleration is given by a=-4x
i think i am confident with a) and d). But i dont know how to do b) and C). can someone please show me how? and just verify what i have done for a) and d). thanks
initial velocity: when t=0
initial acceleration: when t=0
d) prove a=-4x
Otherwise, find a relative maximum of the displacement curve. Since you are dealing with the sine function, the displacement will be the same at every relative maximum, so just pick one. Remember that relative extrema occur only at critical points (i.e., where the derivative is zero or undefined). Find your critical points and apply the first or second derivative test.