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A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's position vector in m at instant the x-component of the velocity vector vx = 8 m/s.

Question

A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's position vector in m at instant the x-component of the velocity vector vx = 8 m/s.

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Step 1
Write the expression for velocity
-I(5+5)dt
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Write the expression for velocity -I(5+5)dt

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Step 2
Equate the x-component of velocity to 8 m/s
(8 m/s)
1.686 s
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Equate the x-component of velocity to 8 m/s (8 m/s) 1.686 s

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Step 3
Integrate velocity to find position
6
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Integrate velocity to find position 6

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