# One dimensional motion

I was recently solving a question which is as follows: Displacement in a straight line motion varies as s=6+12t-2t^2. What distance will be covered in first five seconds? I, actually, got stuck in between. Velocity finds a relation v=12-4t, which gives zero velocity at t=3 seconds. This means that it will change its direction after three seconds, and so the displacement and the distance travelled till three seconds should be equal. Now, can we put 3 in the first relation to get the displacement? If yes, then I got the value of s to be 24. But if I calculate s using velocity relation(using other two equations of motion) I am getting 18. What's the reason ending up this way? Kindly correct me if I am wrong.