The Meaning of Acceleration. Constant and Non-Constant Acceleration. Gravitational Acceleration

In these revision notes for The Meaning of Acceleration. Constant and Non-Constant Acceleration. Gravitational Acceleration, we cover the following key points:

• What are motion maps and what are they used for?
• What is acceleration and how can we calculate it?
• What is deceleration and how it relates to the acceleration?
• What is constant and non-constant acceleration?
• What is the average and instantaneous acceleration and when should we use them?
• What is gravitational acceleration and what is its value near the Earth surface?

The Meaning of Acceleration. Constant and Non-Constant Acceleration. Gravitational Acceleration Revision Notes

In Kinematics, Motion Maps are a useful visual tool for analysing and demonstrating what we know about how an object moves. In general, a motion map can represent the position, velocity, and acceleration of an object at various clock readings.

A motion map has many similarities with a motion graph. They both have a origin (reference point), a positive and a negative direction and they both include units. The only difference is that a motion graph doesn't show any object but only numbers. On the other hand, a motion map shows the moving object and the way how it is moving is shown through arrows. Longer the arrows, faster the object is moving.

By definition, "Acceleration is the rate of velocity change per unit of time."

The term "Rate" means "something changing with time." Therefore, if the change in velocity ∆v⃗ = v⃗₂ - v⃗₁ occurs during a time interval ∆t, we obtain the formula of acceleration a⃗:

Since velocity is measured in m/s and time in s, the unit of acceleration is

Acceleration is a vector quantity as it is obtained by dividing a vector (∆v⃗) by a scalar (Δt).

When the velocity changes at the same rate, we have a motion with constant acceleration, otherwise, the acceleration is not constant and, in this case, it is better to consider the average acceleration.

On the other hand, the instantaneous acceleration shows the acceleration at a given instant, similarly to the concept of instantaneous velocity. Thus, if we are required to find the instantaneous acceleration in a certain instant t, we need to consider a very narrow time interval Δt around the given instant and calculating the respective velocities v⃗₁ and v⃗₂ for the two bordering points of the interval. Then, using the equation

we find the value of the instantaneous acceleration.

If the object slows down, we say it is decelerating. Deceleration is the opposite of acceleration, i.e. it is a "negative acceleration." In such cases, the velocity decreases with time, i.e. the values of velocity in the successive intervals are smaller than those in the previous ones. This means the change in velocity is negative as in the expression ∆v⃗ = v⃗_{i + 1} - v⃗_i (where i represents the number of the interval considered), the successive value of velocity (v⃗_{i + 1}) is smaller than the previous one (v⃗_i). Thus, when dividing a negative number (∆v⃗) by a positive one (Δt) the result is negative.

It is a known fact that Earth causes an attraction effect on objects near its surface. This attraction effect causes a downward acceleration as object move faster and faster as they approach the Earth surface. If we neglect the opposing effect of air (air resistance), we consider this acceleration as constant. It is known as the "gravitational acceleration" or the "acceleration of free fall." It is denoted by g⃗ and has a value 9.81 m/s² near the Earth surface. We get the value of gravitational acceleration as (+ 9.81) m/s² when falling down and (- 9.81) m/s² when moving up (as the Earth attraction in this case opposes the motion and as a result, the object slows down).