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The position of a particale is , vec r =...

The position of a particale is , `vec r = 2. 0 t hati + 3. 0 t ^(2) hatj + 8.0 hatk`
where t is in seconds and coefficients have the proper units for r to be in metre Find v (t) and a (t). Also find the magnitude of v (t) at = t = 2.0 s.

Text Solution

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Velocity, `vecv (t) = (vec (dr))/(dt) = ( d)/(dt) ( 2 . 0 t hati + 3. 0 t ^(2) hatj + 8. 0 hatk ) = 2. 0hati + 6. 0 t hatj`
Accelertaion , `veca (t) = ( vec (dv))/( dt ) = 6 hati `
At `t = 2. 0 s, vec v = 2. 0 hati + 6. 0 xx 2 hatj = 2 . 0 hati + 1 2 hatj`
`v = sqrt (2 ^(2) + 12 ^(2)) = sqrt ( 148) -= 12.1 ms ^(-1).`
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