A particle is moving with the given data. Find the position of the particle. a (t) = 2t + 9, s (0) = 8, v (0) = - 7

If you mean by a (t) = 2t+9 is the acceleration function then we integrate ...

v (t) = 2t^2/2+9t+c where c is vo and we are told that that is - 7 so

v (t) = t^2+9t-7 integrating again we get:

s (t) = t^3/3+9t^2/2-7t+c where c is the initial position which is 8 so

s (t) = t^3/3+9t^2/2-7t+8 which neatened up as

s (t) = (2t^3+27t^2-42t+48) / 6