How do I approach a SUVAT question in mechanics?

This question is best solved through a worked example: A train travels along a straight piece of track between 2 stations A and B. The train starts from rest at A and accelerates at 1.25m/s^2 until it reaches a speed of 20m/s. It then travels at this speed for a distance of 1560m and then decelerates at 2m/s^2 to come to rest at B. A) find the distance from A to B B) find the total time take for the whole journey  The first thing that you do with any SUVAT question is write down the 3 equations of motion that we know. It's important to memorise these, they come up so I'm going to ask you to tell me these equations at the beginning of each session! It is also important to note that these equations are only valid when the acceleration is constant. Now, to break down this question it will be very usefulk to draw a velocity, time graph of what's happening. The first part of the question gives a constant acceleration of 1.25 metres per second squared. If something is accelerating at a constant rate, what does this mean about the velocity? We can therefore draw a linear increase in acceleration for part 1 of the train's journey. It then reaches 20 metres per second so we can label this on our graph. We now have a constant speed of this 20 metres per second for 1560 metres, which we can add to the graph as part 2. Now onto solving part A, I said that you can only use the SUVAT equations when accereration is constant. If we look at the graph, is this the case here? Is there anywhere where acceleration is constant? Well, in that case we can use the SUVAT equations separately on parts 1, 2 and 3. We write out each term (s, u, v, a and t) and then substitute the values that we know in... We then add these separate parts together to find the total displacement, s. We do the same for part B of the question, let's see you work through this part.