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A radius vector of a point A relative to...

A radius vector of a point A relative to the origin varies with time t as `r=ati-bt^2j`, where a and b are positive constants, and i and j are the unit vectors of the x and y axes. Find:
(a) the equation of the point's trajectory `y(x)`, plot this function,
(b) the time dependence of the velocity v and acceleration w vectors, as well as of the moduli of these quantities,
(c) the time dependence of the angle `alpha` between the vectors w and v,
(d) the mean velocity vector averaged over the first t seconds of motion, and the modulus of this vector.

A

`vec omega = 2a hatj`

B

`vec omega = 2b^(2) hatj`

C

`vec omega = 2bhatj`

D

`vec omega = -2bhatj`

Text Solution

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The correct Answer is:
D
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