A particle moves along the x-axis with the given acceleration function a(t) = 8t - 6, initial position s(0) = 2, and initial velocity v(0). Find the position function.

Step-by-step explanation:

Relation between acceleration, velocity and position:

The velocity function is the integral of the acceleration function.

The position function is the integral of the velocity function.

Acceleration:

As given by the problem, the acceleration function is:

Velocity:

In which the constant of integration K is the initial velocity, which is v(0). So

Position:

The initial position is s(0) = 2. So

it has the same slope and a different y-intercept

hope this : )

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step-by-step explanation: