The final mathematical quantity discussed in Lesson 1 is acceleration. An often misunderstood quantity, acceleration has a meaning much different from the meaning sports announcers and other individuals associate with it. The definition of acceleration is:
Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity.
Constant Acceleration
Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned before, the data above shows an object changing its velocity by 10 m/s in each consecutive second. This is known as a constant acceleration since the velocity is changing by the same amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled! If an object is changing its velocity – whether by a constant amount or a varying amount – it is an accelerating object. An object with a constant velocity is not accelerating. The data tables below depict motions of objects with a constant acceleration and with a changing acceleration. Note that each object has a changing velocity.
Since accelerating objects are constantly changing their velocity, you can say that the distance traveled divided by the time taken to travel that distance is not a constant value. A falling object for instance usually accelerates as it falls. If you were to observe the motion of a free-falling object (free fall motion will be discussed in detail later), you would notice that the object averages a velocity of 5 m/s in the first second, 15 m/s in the second second, 25 m/s in the third second, 35 m/s in the fourth second, etc. Our free-falling object would be accelerating at a constant rate.
Calculating Acceleration
The acceleration of any object is calculated using the equation:
