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A particle moves in the x-y plane with constant acceleration. At time zero, the particle is...

A particle moves in the x-y plane with constant acceleration. At time zero, the particle is at r = <5.0, 2.0> m and has velocity v = <-4.0, 9.0> m/s. The acceleration is constant and is given by a = <4.0, 6.0> m/s2 . (a) Find the velocity at t = 2.0 s. (b) Find the position at t = 4.0 s. Give the magnitude and direction of this position vector. (c) Sketch (approximately to scale) the vector diagrams for vi , vf , and ?v, and for ri , rf , and ?r

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Expert Solution

a) Find the velocity at t = 2.0 s.
we have, velocity v = u+at u is the initial velocity,
               so             v = <-4.0, 9.0> + <4.0, 6.0>*2

                                   = <4.0, 21.0> m/s

(b) Find the position at t = 4.0 s. Give the magnitude and direction of this position vector.

                     = r0 + ut + (1/2)at2 = <5.0, 2.0> + <-4.0, 9.0>*4 + (1/2)<4.0, 6.0>*42

                                                        = <21.0, 86.0>

(c) Sketch (approximately to scale) the vector diagrams for vi , vf , and ?v, and for ri , rf , and ?r

genius_generous answered 6 months ago
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