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.
Your equation defines position not displacement. So when you put the value of time in the given equation.you get distance from the origin. Add the value of initial position in your second answer you will get same result as in first case