The APsolute RecAP: Physics 1 Edition is a guided review through all ten units of classical mechanics.
Episode 3 recaps how physics is able to use algebraic and graphical language to provide quantitative descriptions of objects in motion. We step on the gas to describe distance, displacement (2:00) and acceleration (5:42). Can you identify a vector? (7:00)
The Question of the Day asks (8:00 ) A car driving to the left with a velocity of -33.3 m/s slows to rest in 3 seconds. What is the acceleration of the vehicle? Don’t forget to include a sign to indicate direction.
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Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on 1-Dimensional Kinematics and introduce the concepts of displacement, velocity, and acceleration.
Lets Zoom out:
Unit 1: Kinematics
Topic 1.1
Big Idea: Force Interactions
You are stopped at a red light patiently waiting for the signal to change so that you can proceed. Once the light turns green, you press on the gas pedal and 6 seconds later you realize that you have reached the 120 km/h (or 33.3 m/s) speed limit and should probably not go any faster. You notice on your car’s odometer, that you traveled exactly 0.1 kilometer (or 100 m) during this time. This is a narrative description of 1-D kinematics. A story-like explanation of an object and its motion. While this is often enough in our everyday lives, it is not adequate in Physics because it does not allow us to quantitatively know very much about your car, and it does not offer us the ability to predict the future motion of the car. Physics is able to use algebraic and graphical language to provide quantitative descriptions of objects in motion.
Lets Zoom in:
In order to learn more about the car at the red light, we have to agree on some common ground rules. First, the entirety of the car is located at a single point, this is known as a point mass. Second, the road that the car is driving on is stationary compared to the car. This is our frame of reference. Finally, the forward direction will be positive, and therefore the reverse direction will be considered negative.
Normally, we would say that the car traveled a distance of 100 m. Unfortunately, knowing the car traveled for 100 m on the odometer isn’t actually all that helpful to be able to know where the car is located compared to its starting location. Did it travel that distance by doing a circle? Did the driver shift the car into reverse? Maybe the driver drove forward 75 m, and backward the last 25 m! In order to sort out confusion, in Physics we say that the car had a displacement of +100 m. The positive sign will indicate the direction of the motion. In our example, it will be forward. Even more specifically, we can imagine that the car had an initial position at the origin or 0.0 meters, and traveled to a final position of +100 m. We find the displacement by taking the final position and subtracting the initial position. As a result we have a displacement of +100m - 0m or +100 m. Looking at the earlier suggestion of the 75 m forward and then 25 m in reverse so they would end 50 m from their starting point, the car in that case would travel a distance of 100 m, but the displacement would be final position (+50 m) - initial position (0 m) for a displacement of +50 m. See the difference? Displacement is a change in position and answers the questions, “How much did the position change?, and which direction?” while distance only answers, “How far?” Displacement is our first example of a vector, a measurement that has both magnitude and direction. The magnitude is the number portion with the unit or the size of the measurement, the positive sign is the direction portion.
Another way to think about displacement is when you wake up in the morning and go to school all day, and then return home in the evening. You traveled a distance throughout the day, your step-counter will say so, however your displacement was 0 m by the end of the day and the GPS reading of your starting and final location would indicate the same position at morning and at nighttime.
Sticking with the example of driving 100 m by going forward 75 m and then in the reverse direction 25 m, we can also utilize what we know about the duration of the trip or the time that elapsed. Most people know that they can figure out the speed of an object by dividing distance by time. In our example, the car drove 100 m in 6 second, therefore the average speed was 16.7 m/s. It shouldn’t come as a surprise that physicists also have a more specific method here too. The term average velocity is the displacement divided by time. So, in our example we would have +50 m / 6 seconds or +8.3 m/s. Here again we use a positive sign to indicate the direction of the motion. So, velocity is another example of a vector. Speed is “how fast” while velocity is “how fast and which way.” Average velocity is important, but it isn’t the full story. It only tells us what the driver did on average throughout the entire 6 seconds, but we know he was stopped and then he was moving more quickly, so he couldn’t have driven at only +8.3 m/s. This is because we have the even more descriptive initial and final velocities for the car. We will revisit those in the next episode, but what you need to know is that our current method of displacement divided by time just isn’t describing the full picture, and we need more tools to do so.
Finally, and often the most confusing is the fact that the car accelerated. The reason this concept can be troubling is that we already use it in everyday language to generally mean “speed up.” As is always the case with Physics, there is more to it! Sure speeding up is an acceleration, but so is slowing down, and strangely enough so is making a turn (OoOoOoO foreshadowing). Acceleration is a measure of how quickly you change your velocity, or change in velocity divided by elapsed time. For the car at the red light, it went from an initial velocity of 0.0 m/s to a blistering final velocity of +33.3 m/s over the course of 6 seconds. So, we would say that the car had a velocity change of +33.3 m/s - 0 m/s over 6 seconds or +5.6 m/s^2. A really good way to think of acceleration is that if there is a push or pull, then there is an acceleration. In our car example, it is easier to imagine that the car picked up speed when the light turned green not because of any motor in the car, but because someone or something pushed it from behind. It should be understood that the direction of the acceleration matches the direction the car was pushed in, forward or positive, and sure enough we see that in our +5.6 m/s^2 acceleration. Now, if the car slowed down for a stop sign or another red light, then the push would now need to be in the opposite direction and therefore it would be negative. Like displacement and velocity, direction matters, and acceleration is… you guessed it, a vector. That’s it!
To recap……
Displacement is a change in position, velocity is a change in position over time, and acceleration is a change in velocity over time. All three can occur in the positive and negative directions. Measurements that are direction dependent are known as vectors. Displacement, velocity, and acceleration are all vectors that we will get to know much better in the next few episodes.
Coming up next on the APsolute RecAP Physics 1 Edition: Graphical representations of one dimensional kinematics.
Today’s Question of the day is about acceleration.
Question: A car driving to the left with a velocity of -33.3 m/s slows to rest in 3 seconds. What is the acceleration of the vehicle? Don’t forget to include a sign to indicate direction.