Question

A particle is moving with acceleration a(t)=12t+14 . its position at time t=0 is s(0)=16 and its velocity at time t=0 is v(0)=16 . What is its position at time t=14 ?

Answer 1

Integrate acceleration to get velocity and integrate velocity to get the displacement or position.

Answer 2

When you integrate a(t)dt to find v(t) it will be an indefinite integral. That means you need to add a constant C1. The value of C can be found by applying the initial condition v(0)=16.

Repeat the process and integrate v(t)dt to get s(t).

Again this indefinite integral will require you to add another constant C2. The value of C2 can be found by applying the initial condition s(0)=16.

After that you will have a specific formula for s(t), to which you can plug in t=14 to find the position at that point.