Preparation:
In daily life, we say that a car is accelerating when its speed is increasing. When a car maintains constant speed while going through a turn or when its speed is decreasing in braking, ordinarily we would not say that the car is accelerating. However, the concept of acceleration as used in physics is defined so that the car has a non-zero acceleration in all of these cases.
Acceleration is a central concept in mechanics because the central law of motion, Newton's second law, relates the acceleration of an object to the forces acting on the object. For this law to be true, acceleration must be defined the way it now is in physics. You need to understand this definition in order to be able to understand and apply Newton's second law of motion.
The concept of acceleration is derived from that of velocity, but it is not the same as velocity. Both of them are vector quantities. Can you think of a motion in which the acceleration vector is not in the same direction as the velocity vector at every instant? An example will be shown on Page 2.