In Kinematics we describe the motion only. We know the velocity or acceleration, or we know the dependence of velocity on time or acceleration on time, and we need to find something else about this motion.
For example, we know that the velocity is 30 mph during 5 hours and 50 mph during 1 hour and we need to now the traveled distance. We do not know why the velocity is constant; we do not know why the acceleration has a given value. We do not know the origin of the motion. These questions are addressed in Dynamics. In Kinematics we just need to find the parameters of the motion – relation between velocity, acceleration, and distance.
Usually only two types of motions are considered in kinematics problems:
- Motion with constant velocity and
- Motion with constant acceleration.
Motion with variable acceleration is quite complicated problem. Only in some special cases we can easily solve such problems, but usually we need to solve second order differential equations to get the answer in these problems.
All the equations of motion in kinematics problems are expressed in terms of vectors or coordinates of vectors. And this is the most difficult part in kinematics problems: how to express the initial values or the final values in terms of the variables in the kinematic equations. Another difficult part in kinematic problems is related to the description of relative motion.
You can read about the kinematics problems with the detailed solutions of many kinematics problems here: "Physics Problems: Kinematics ".