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Jim has taught undergraduate engineering courses and has a master's degree in mechanical engineering.

This lesson describes the difference between speed, velocity and acceleration. Examples are used to help you understand the concept of acceleration and learn to calculate acceleration with a mathematical formula.

Acceleration

Did you know a jet can be traveling at the speed of sound and not be accelerating? While the speed of sound is extremely fast, acceleration occurs only if the jet is speeding up or slowing down. Let's take a look at a quick example to understand the difference between speed and acceleration.

When I take off in my car, I accelerate until I achieve my maximum speed. I cease to accelerate when I obtain a constant speed. The law states that I can drive at a maximum speed of 65 miles per hour on a highway in Oregon. The law doesn't put a restriction on my acceleration. If I floor the accelerator, I may be able to achieve 65 miles per hour in about 7 seconds. If I go easy on my minivan, it will take me closer to 14 seconds to achieve the same speed.

By flooring the accelerator, I decrease the time it takes to change my speed from 0 to 65 miles per hour. In other words, my acceleration is greater. The entire time my speed is increasing from 0 to 65 miles per hour, I am accelerating. The moment I achieve 65 miles per hour and ease up on the gas to keep a constant speed, I am no longer accelerating.

Definition of Acceleration

Before we can talk about acceleration, we need to understand velocity which is the rate that an object moves from one place to another. Velocity is a vector quantity, which means it has both a magnitude, called speed, and a direction.

If I were in my car traveling 30 miles per hour to the north, the magnitude of my velocity, or speed, would be 30 miles per hour, and my direction would be north. If I changed my speed or if I changed my direction, then I would experience a change in my velocity. This is where acceleration comes into play.

Acceleration, also a vector quantity, is the rate at which an object changes its velocity. The most obvious way that I could accelerate would be to change my speed from say 30 miles per hour to 40 miles per hour. However, I would also experience acceleration if I changed direction without changing my speed, like driving around a bend in the road at a constant 30 miles per hour. In a large bend where my direction was changing slowly, I would experience a lower acceleration than if I were to take a sharp turn, since my direction would change more rapidly. We can feel the difference in acceleration when we go around a corner in a car as a sensation that we're being pulled or pushed to one side or the other.

Example of Acceleration

Consider a person riding a bike. Let's say that they start out from rest and reach a speed of 10 meters per second by 1 second, 15 meters per second by 2 seconds and 18 meters per second after 3 seconds. We know that the bike accelerated for the entire 3 seconds since the velocity kept increasing, but was the acceleration the same for each time period? To find out, we'll need to use the change in velocity over each period of time to calculate the average acceleration.

Calculating Average Acceleration

Now that we understand the concept of acceleration, the formula for calculating acceleration will make sense and be easier to remember. The average acceleration of an object can be calculated using the following equation:

a = (vf - vi) / (tf - ti)

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where, a = average acceleration, vf = final velocity, vi = initial velocity, tf = final time and ti = initial time. In other words, acceleration equals the change in velocity divided by the change in time. Let's plug in some numbers from our bike example. We can calculate the average acceleration of the bike during the first second.

Recall the formula for acceleration a = (vf - vi) / (tf - ti)

a = (10 m/sec - 0 m/sec) / (1 sec - 0 sec) a = (10 m/sec) / (1 sec) a = 10 (m/sec) / sec a = 10 m / (sec*sec) a = 10 m/sec^2

Now, let's calculate the average acceleration during the next second.

a = (15 m/sec - 10 m/sec) / (2 sec - 1 sec) a = (5 m/sec) / (1 sec) a = (5 m/sec) / sec a = 5 m / (sec*sec) a = 5 m/sec^2

And finally, we'll calculate the average acceleration during the third second.

a = (18 m/sec - 15 m/sec) / (3 sec - 2 sec) a = (3 m/sec) / (1 sec) a = 3 (m/sec) / sec a = 3 m / (sec*sec) a = 3 m/sec^2

As you see, the acceleration was different over each time period. In the first period between the start and 1 second, the acceleration was the highest, and the velocity changed the most. By the third second, our cyclist was getting tired and had the lowest acceleration, resulting in the smallest change in velocity.

The units for acceleration are distance/time^2. For example, m/sec^2 or miles/hour^2. Since acceleration is the change in velocity over a time period, the units for acceleration can be expressed as velocity units divided by time units; for example, (m/sec) / sec, which can be simplified to m/sec^2.

Lesson Summary

To summarize, acceleration is the rate at which an object changes its velocity. Velocity is the rate at which an object moves from one place to another. Simply put, an object accelerates if its velocity is changing. Both acceleration and velocity are vector quantities as they are fully described with both magnitude and direction. The average acceleration of an object can be calculated using the following equation:

a = (vf - vi) / (tf - ti)

where a = average acceleration, vf = final velocity, vi = initial velocity, tf = final time and ti = initial time. The units for acceleration are distance/time^2; for example, m/sec^2.

Learning Outcomes

You'll have the ability to do the following after this lesson:

Define acceleration, velocity and vector quantity

Explain the difference between speed and acceleration

Identify the formula for calculating the average acceleration of an object and the units for acceleration

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