I am having considerable trouble getting my head around questions involving the SUVAT equations. I can do them if I split them into up and down parts but I'm supposed to be able to do then in single steps and I'm finding that really difficult.
Here is an example:
A stone is projected vertically upwards from a point A with speed ums-1. After projection the stone moves freely under gravity until it returns to A. The time between the instant that the stone is projected and the instant that it returns to A is seconds. Modelling the stone as a particle. Show that u = .
It seems to me that while the stone is moving upwards then it's acceleration, a, is -9.8 ms-2, but once it has reached it's maximum height and starts falling under gravity it's acceleration is 9.8 ms-2. How can I use an equation with 'a' in it if it's sign is changing? Also if is consider 'u' to be positive then 'v', once the particle is falling, must be negative. I don't understand how that works with the equations of motion.
Any help would be very much appreciated.