Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration. a particle moves along the x-axis at a velocity of v(t) = 5/√t, t > 0. at time t = 1, its position is x = 12. find the acceleration and position functions for the particle.

We know that the acceleration of the particle is defined as

Since it is given that

Now by definition of velocity we have

Integrating on both sides we get

Applying values we get

To find the constant we note that at t=1 the particle is at x=12 Thus applying values in the above equation we get

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