Final answer:
A 2 kg body moves along the x-axis under the influence of a force -6x Newton, causing its acceleration at any position x to be -3x m/s². As the acceleration varies with the position, the velocity of the body will also change with its position.
Step-by-step explanation:
The subject of this question is a body moving along the positive x-axis, subjected to a force and its corresponding motion. According to Newton's second law of motion, force (F) equals mass (m) times acceleration (a), or F = ma. In light of this, the force acting on the given moving body (where fx = -6x newtons, and x indicates the position on the x-axis) is variable, changing in direct proportion to the body's placement on the x-axis. Given the fact that the body in question has a mass of 2 kg, we can apply the concept of the force equation to determine the acceleration of the body at any given point on the x-axis. To do this, divide the neither-6x force by the 2 kg mass to establish the acceleration at any point x (a = fx/m = -3x m/s²). To figure out the final velocity, we have to integrate the acceleration function, but the initial condition (velocity at x = 3.0 m is 8.0 m/s) must be kept in consideration.
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