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Determining the Acceleration of an Object

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  • 0:04 What Is Acceleration?
  • 2:38 Calculating Acceleration
  • 5:17 Free Fall
  • 6:56 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Acceleration is a change in an object's state of motion. A few variables need to be identified to calculate an object's acceleration, but once we have those values, we can put them into a simple equation to find out how quickly or slowly an object's velocity is changing.

What Is Acceleration?

Galileo Galilei is a pretty important guy when it comes to the world of physics. For example, he discovered the concept of inertia, which is an object's tendency to resist change in its state of motion. He also described speed and velocity, which is the speed and direction of an object. These concepts seem simple to us today, but during Galileo's time, these ideas were quite novel.

One of the reasons Galileo was so successful as a scientist was his diligent use of experiments. Testing hypotheses and ideas allowed him to support his results and conclusions with more than just logic and reasoning. He could actually show how things worked in our physical world.

In addition to his velocity experiments, Galileo also looked at the movement of objects down inclined planes. What he found was that a ball rolling down an incline rolled faster and faster as it went. This meant that the velocity of the ball changed because the speed of the ball was changing. But what he also found was that the ball gained the same amount of velocity in equal time intervals - in each second the ball was rolling, the velocity increased by the same amount.

This rate of change of velocity is called acceleration. Much like speed is the change in distance over a time period, acceleration is the change in velocity over time. Acceleration can describe both an increase and a decrease in an object's speed.

When you push the gas pedal in your car (also known as the accelerator!), your car speeds up - you change its velocity. But when you put your foot on the brake and slow the car down, you are also changing the velocity and therefore the acceleration. However, even though both are acceleration, we often use the term deceleration to describe a decrease in an object's velocity.

You can also change the car's acceleration by turning its steering wheel. Since velocity includes direction, and turning your car changes its direction, you are changing the car's velocity even if you don't change the speed. Since acceleration is a change in velocity, the change in direction means the car is accelerating. So acceleration can be a change in speed, direction, or both! But remember, zero acceleration does not mean zero velocity. It simply means that the object will maintain its velocity - it doesn't speed up, slow down, or change direction.

Calculating Acceleration

Determining an object's acceleration is pretty straightforward. You already know that acceleration is change in velocity over time, and we can represent these words with an equation: a = ΔVt (the Greek letter Δ means 'change in'). Here, a is the acceleration, V is the velocity, and t is the time. All you have to do now is plug in your values and do the math.

Let's turn to Galileo's inclined plane to see how this works. If Galileo places a ball at the top of the ramp and lets it go, the ball will start rolling down, and its velocity will increase. In the first second, the ball goes from 0 meters per second (m/s) to 2 m/s. In that second second of rolling, the ball goes from 2 m/s to 4 m/s. If it continues on in this steady increase, the change in velocity for the ball is 2 m/s each second.

Plug that in to our acceleration equation and we get: a = (2 m/s ) / (1 s). Once we do the math, we find our acceleration to be 2 m/s*s. The units of time do not cancel because there is time in the velocity (distance over time) and in the time of the acceleration. So our final answer looks like this: a = 2 m/s2.

Let's look at another example. Say you are driving, and in one second you steadily increase your velocity from 25 kilometers per hour to 50 kilometers per hour. In the next second, you increase your velocity from 50 km/h to 75 km/h. If you kept up this steady increase, you can see that your velocity changes by 25 km/h each second.

To use this in our equation, we would have: a = (25 km/h) / (1 s). When we solve this, we get 25 km/h*s. Since there are 3600 seconds in an hour, we can convert the time units so that they are the same: 25 km/(3600s * s) = 0.0069 km/s2. What this means is that your velocity is changing by 0.0069 km/s per second - in each second your velocity changes by that amount.

Free Fall

Falling objects (as well as those traveling upward from the ground) also have acceleration because they experience a change in speed, just like the balls rolling down the ramp in Galileo's experiments.

What's interesting about falling objects is that they all have the same acceleration when air resistance doesn't affect the object's motion, also known as free fall. The rate of change in velocity for free-fall is 9.8 m/s2, which means that the object gains speed as it falls at the rate of 9.8 m/s each second.

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