Question

Suppose that an object's acceleration functions is given by a=8t+5. the objects initial velocity 4, and the initial position is 12. find the object's displacement as a function of time.

Answer 1

You take the antiderivative of acceleration twice putting in initial values where appropriate as constants of integration.
a=8t+5
v=4t^2+5t+4
s=4/3t^3+5/2t^2+4t+12