One such distinction is between velocity and acceleration. A big aha! Now we know why rocket launches that seem so slow gain enormous speeds when high and out of sight.ĭistinguishing between related concepts is a challenge in physics. Initial acceleration is sluggish, but with time, fuel turns to exhaust and the mass of the rocket decreases with a correspondingly increasing acceleration that puts it into orbit. Their initial mass before launch is mostly the mass of its fuel. This physics is enormously important for rockets. For the same applied force, greater mass means less acceleration. The equation a = F/m tells us why an automobile with a full tank of gas will accelerate less then when the tank is nearly empty. It tells us that the acceleration of an object is directly proportional to the net force on the object, and is inversely proportional to the mass of the object. Why objects accelerate is answered by Newton’s second law, sometimes called the law of acceleration. Then you can treat the distances covered in free fall. Move on! An aha! is that your course can get up to rainbows and other physics goodies before the course-time bell rings!Ī follow-up to speeds of fall is assigning an odometer to the falling speedometer. In the spirit of “wisdom is knowing what to overlook,” tell your class that in their study of physics, for some students, all will not be fully understood, and that to keep on your scheduling quest to advance to other physics goodies, you’ll not spend time on what could better be spent in a math class. If you still have some puzzled students, my advice (nurtured by many years of teaching) is to NOT devote more class time to it. Or, remind them of a rule of arithmetic that says when dividing a fraction by a number (m/s ÷ s), invert the number and change the division sign to a multiplication sign. You can expect that some students will be uncomfortable with the symbol for second appearing twice in m/s 2-first for velocity and again for the time that velocity changes. We say the boulder and speedometer fall with constant acceleration. During each second of free fall, the exact same pickup of speed occurs. Again, to simplify calculations, we round free-fall acceleration that is customarily expressed as 9.8 m/s 2 to 10 m/s 2. We can express this as 10 m/s per second, or, 10 m/s/s, which is read as 10 m/s squared, or in math notation, 10 m/s 2. So what’s the value of ∆ v/∆ t for the falling boulder? Another Aha! It’s 10 m/s per every 1 second. This represents another small aha! moment, for it’s easy to see a 10-m/s increase for each second of fall.Įxpressed in delta notation, for every ∆ t of one second the gain in speed ∆ v is 10 m/s. Ask your students what the change in speed is during each 1-second interval of fall. In two seconds the speedometer reads 20 m/s. One second later the reading is 9.8 m/s, which we’ll round off to 10 m/s (multiples of 10 are easier to handle). Dropped from rest, the initial reading is zero. Only the force of gravity acts on the boulder and its speedometer without air drag, it is in free fall. I’ve found that a great way to visualize acceleration is imagining a speedometer attached to a boulder dropped from the edge of a high cliff, which I featured in the March 2019 Focus on Physics article (Figure 1). Maybe a small aha! if students can articulate this, and go further and and say what it means. We can express the equation for acceleration as a = ∆ v/∆ t, which is read: Acceleration is equal to the change in velocity per change in time. The challenge for students is coming to terms with the idea of “time rate of change.” We introduce the symbol ∆ (delta) to denote “change in.” A change in velocity is expressed ∆ v a corresponding change in time is ∆ t. He defined velocity as the time rate of change of distance, and further defined acceleration as the time rate of change of velocity. Galileo was the first to introduce the concept of acceleration. How to teach it is featured in my March 2019 Focus on Physics article “Quickly Teaching Speed, Velocity, and Acceleration-Part 2.” This article extends that by highlighting some of the gems associated with teaching acceleration. Maybe it’s fine to hurry through speed and velocity, but teaching acceleration should be allotted additional time. That’s because speed and velocity are intuitive, while acceleration is not. Teaching acceleration is decidedly a bigger challenge than teaching speed and velocity.
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