A09 and A10. The velocity of a particle is given by v = i(9t 2 12) + j(4t 12), w

Question

A09 and A10. The velocity of a particle is given by v = i(9t2 12) + j(4t 12), where 10 t +10 . At time t = 2 seconds the particle is has coordinates ( x, y) = (0,0) . A09 Find the position coordinates of the particle at time t = 0.

A10. During the specified time interval, is the acceleration vector is parallel to the y-axis at any time? If not, explain clearly why this is so. If at some time the acceleration vector is parallel to the y-axis, explain why this is so and find the time at which this condition occurs.

Explanation / Answer

v = i(9t2 12) + j(4t 12)

r = integration(v * dt)

r = integration(i(9t2 12) + j(4t 12))

r = (3t^3 - 12t) i + j *(2t^2 - 12 * t ) +r0

as t = 2 , r = (0 ,0)

0 =( 3 * 2^2 - 12 * 2) i + j *(2 *2^2 -12 *2) + r0

r0 = 12 i + 16 j

the position at t = 0 is (12,16)

A10)

a = dv/dt

a = d/dt(i(9t2 12) + j(4t 12))

a = 18 t i + 4 j

at time t = 0 s

acceleration = 4 j which is parallel to y - axis

hence , at time t = 0 s

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