Acar starts from rest at a stop sign. it accelerates at 2.0 m/s^2 for 6.0 seconds, coasts for 2.1 s , and then slows down at a rate of 1.5m/s^2 for the next stop sign. how far apart are the stop signs?

Explanation:

We divide the problem in 3 parts: part 1 when the car accelerates, part 2 when its velocity is constant and part 3 when it slows down and we use the main equations for accelerated motion and , and for the last part

We start calculating the displacement and final velocity of part 1 considering the initial velocity is zero:

Now we calculate the displacement of part 2 considering the velocity remains constant since acceleration is zero:

Now we calculate the displacement of part 3 considering the initial velocity is the final velocity of the previous part and that it slows down until coming to rest:

So our total displacement is

because if the tool that you are using is not balanced it there would be false mass.