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- July 11th 2008, 04:41 AM #1

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## can someone please help me?

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*

- July 11th 2008, 05:15 AM #2

- July 11th 2008, 03:30 PM #3

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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

*a) x=3sin2t*

v=dx/dt

v=6cos2t

a=dv/dt

a=-12sin2t

initial velocity: when t=0

v=6cos2t

v=6cos0

v=6m/s

initial acceleration: when t=0

a=-12sin2t

a=-12sin0t

a=0 m/s^-2

d) prove*a=-4x*

a=-12sin2t, x=3sin2t

-12sin2t=-4(3sin2t)

-12sin2t=-12sin2t

therefore a=-4x

- July 11th 2008, 03:50 PM #4
Looks good to me.

Okay.

If you know your trig well (particularly the sine graph), you should be able to answer this without need for calculus.

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.

i.e., find the times when .

- July 11th 2008, 06:37 PM #5

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- July 11th 2008, 06:47 PM #6