Acceleration

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The maths final quantity which is discussed in Lesson 1 is acceleration. The definition of acceleration can be stated as:

Acceleration can be defined as a vector quantity that defines the rate at which an object changes its velocity. An object is still accelerating if it is changing its velocity time and again.

Occasionally Sports announcers say that a person is accelerating if they are moving fast. Still, acceleration has nothing to do with going fast or slow that is with the speed. A person can be moving very fast or slow and still not be accelerating. Acceleration has to do nothing with changing how fast an object is moving. If an object does not change its velocity then the object is not accelerating. The data which is at the right are representative of a northward-moving object does accelerate. The velocity of the object is changing over the course of time. In fact the velocity is changing by a constant amount - that is 10 m/s - in each second. Anytime an object's velocity is changing the object is said to be in an accelerating motion or it has an acceleration.

Constant Acceleration 

At times an accelerating object will change its velocity by the same amount each time or second. This is then referred to as acceleration which is constant since the velocity is changing by a constant amount each second. With a constant acceleration an object should not be confused with an object with a constant velocity. Don't be fooled by these two confusing terms! If an object is changing its velocity no matter whether by a constant amount or even a varying amount  then it is an object which is accelerating. An object with a constant velocity is not said to be accelerating. We should ponder and note that each object has a changing velocity.

Since objects accelerating are constantly changing their velocity one can say that the distance traveled upon a time is not a constant value. If we keenly observe the motion of a free-falling object that is free fall, we would observe that the averages a velocity of object of approximately 5 m/s in the first second, which is approximately 15 m/s in the second second, which can be said to be approximately 25 m/s in the third second. Our object which is free-falling would be constantly accelerating. Given these velocity which is average values during each consecutive 1-second time interval we can easily say that the object would fall 5 meters in the first second then 15 meters in the second second for a total distance of 20 meters then later 25 meters in the third second for a total distance of 45 meters and 35 meters in the few seconds later for a total distance of 80 meters. 

Acceleration Vector Direction 

Since we already know that the acceleration is a vector quantity, it has a direction associated with it as well. 

whether the object is moving in the direction which is negative or positive.

The general principle for determining the acceleration are mentioned below:

If an object is slowing down then the acceleration in it is in the opposite direction of its motion.

This general principle is usually applied to determine whether the sign of the acceleration of an object is negative or positive, left or right, down and up etc. if we observe multiple different cases then in each case, the acceleration of the object is in the direction which is positive. 

In Example  the object is moving in the direction which is positive direction, that is it has a positive velocity and is speeding up. Thus this object has an acceleration which is positive acceleration. If we see other examples  the object is moving in the negative direction and it has a negative velocity and is slowing down. According to our general principle we can conclude that when an object is slowing down then the acceleration is in the opposite direction as the velocity. Thus the object also has an acceleration which is positive.

Motion which is Circular 

In case of uniform circular motion, that is moving with a speed which is constant speed along a circular path, a particle then experiences an acceleration which is resulting from the change of the direction of the velocity vector, while the magnitude remains same or constant. The derivative of the object of location of a point on a curve with respect to time that is  its velocity, turns out to be exactly tangential to the curve always. We have seen that in uniform motion the velocity in the tangential direction does not change at all and the direction of acceleration must be in radial direction, which is pointing to the center of the circle.