# Basic mechanics question

How do you do the following 2 questions? I haven't been told how to do it by my teacher, I assume you learn it in Add maths which I didn't do...

1) A, B and C are three points lying in that order on a straight line. A body is projected from B towards A with speed 3m/s. The body experiences an acceleration of 1m/s squared towards C. If BC=20m, find the time taken to reach C and the distance travelled by the body from the moment of projection until it reaches C.

2) 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 squared until it reaches a speed of 20m/s. It then travels at this steady speed for a distance of 1.56km and then decelerates at 2m/s squared to come to rest at B. Find:
a) The distance between A to B
b) The total time taken for the journey
c) The average speed for the journey

Any help would be appreciated.
I assume you know the equations of constant acceleration (sometimes called 'suvat' equations... v = u + at and all those)?

1) How long does it take for B to come to a halt? What's the distance travelled in that time? B then continues to accelerate towards C; what distance does it have to cover to get to C?

2) Draw a speed/time graph.
1. As in all mechanics question, produce a sketch of the system. The actual mathematics behind this is fairly straightforward, but the concepts are what is important in this question. The particle is moving in one direction (towards A) but experiences a deceleration in this direction. Therefore, eventually, it's going to decelerate until it begins to accelerate and move in the other direction, finally reaching C.

You'll have to use the equations of motion. Firstly, what are the values of initial velocity, acceleration and displacement? [Take care of the signs]. Substitute these into a suitable equation i.e. one which features the variables you have and need. As for the second part, think of how the particle moves. At the point where it stops in order to reverse direction, what can you say about its velocity? Use this to find the distance travelled from B to this point. Then working out the final distance is fairly straightforward.