Take for example a ball rolling. We can describe its motion in terms of kinematiccs equations. For example, we can calculate the velocity of the ball at any given time if we know its initial speed and its acceleration.
How do we go about doing that?
For this problem, we can actually do it by pure logic. Acceleration is the rate of change of velority with time. so if a particle starts from rest with an acceleration of 10 m/s^2, its velocity would be 10 m/s after one second. Following this, it is purely common sense to say that the velocity of a particle is given by its initial speed + (acceleration x time it has been travelling)!
There is a set of equations which represent these logic in mathematical form. They are:
1) v = u + at
2) v^2 = u^2 + 2as
3)
4) s = ut + (0.5)at^2
so we can actually work out any problem involvin 2-d linear motion with these equations. isn't physics amazing?