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If the position vector of a particle is ...

If the position vector of a particle is given by `vec r =(4 cos 2t) hat j + (6t) hat k m`, calculate its acceleration at `t=pi//4 second `.

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Position, `vec r =94 cos 2t) hat I + (4 sin 2t) hat j + 6t hat k`
Velocity, `vec v =(vec d r)/(dt) = 94 (-sin 2t) . 2} hat I + [4 9cos 2t). Hat j + 6 hat k`
Acceleration, `vec a (vec d v)/9dt) = [-8 9cos 2t) .2] hat I + [8 (-sin 2t). 2] hat j =(-16 cos 2t 0 hat i + (-16 sin 2t) hat j`
Wher `t=pi//4, vec a =(- 16 cos 2xx pi // 4) hat i + (-16 sin 2 pi //4 ) hat j =(-16 cos pi //2) hat i+ (-16 sin pi//2 ) hatj `
`=(-16 xx 0) hat i + (-16 xx 1) hat j = -16 hat j ms^(-22)`.
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