At time t = 0, a particle is at rest in the x‐y plane at the coordinates (x0, y0) = (6, 0) in. If the particle is then subjected to the acceleration components ax = 0.5 − 0.35t in./sec^2 and ay = 0.15t − 0.02t^2 in./sec^2. Determine the coordinates of the particle position when t = 6 sec. Plot the path of the particle during this time period.

(0, 0.04)

Explanation: Given that At time t = 0, a particle is at rest in the x‐y plane at the coordinates (x0, y0) = (6, 0) in. If the particle is then subjected to the acceleration components ax = 0.5 − 0.35t in./sec^2 and ay = 0.15t − 0.02t^2 in./sec^2.

differentiate ax and ay twice. That is, second derivatives to get the position

dax/dt =  − 0.35

d^2ax/dt^2 = 0

and

day/dt = 0.15 − 0.04t

d^2ay/dt^2 = 0.04

the coordinate of the particle after t = 6 sec will be (0, 0.04)

the graph will be linear

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