A particle is moving with acceleration

Question

A particle is moving with acceleration . its position at time  is  and its velocity at time  is . What is its position at time ?

Answer 1

So James H., you integrate the acceleration expression twice with respect to time. Each integration gives you one arbitrary constant; you may best insert these at each integration, using the "initial conditions".

So for the first integration, int[36t + 6]dt = (36/2)t^2 + 6t + C(1). This is the expression for velocity! So if v(0) = 11, we solve for C(1): 18*0^2 + 6*0 +C(1) = 11 ; I think you can handle that?

Then you integrate the complete expression for velocity again, which will require the constant C(2) in a similar fashion, to give you the position expression. Then you plug in to find your answer.

If this is all new material to you, it's time to find a regular tutor to walk you through integration and differentiation.

-- Cheers, --mr. d.