CONCEPTUAL PHYSICS › CHAPTER 3, LINEAR MOTION
Motion Is Relative, and Then It Gets Interesting
Nothing is simply moving. A thing moves with respect to something else, and you have to say what. Once you have said it, the rest of this chapter is four careful distinctions, and every one of them is a distinction students think they already understand.
Say what a motion is measured with respect to, and why that choice changes the answer.
Tell instantaneous speed from average speed, and speed from velocity.
Say what accelerating means, including the two cases that are not speeding up.
Read a graph of position against time by its shape, before measuring anything.
1. Motion is relative
Sitting in your chair you are still with respect to the room, and moving about thirty kilometers every second with respect to the sun. Both are true. Neither is the answer on its own, because the question was incomplete.
When you say a car is doing sixty, you mean with respect to the road. Nobody says so out loud, which is exactly why the idea is easy to miss. It only becomes visible when two observers disagree, and the useful thing is that they can both be right.
The bus, the passenger, and the sidewalk
A bus drives past at a steady speed while a passenger walks along the aisle. Drag the passenger to change how fast they walk, and press the button to change who is measuring. Nothing about the passenger changes when you switch observers. The number does.
2. Speed: how fast, and over what
Speed is how much ground you cover in how much time. The speedometer shows your speed right now, which is the instantaneous speed. The whole trip divided by the whole time is the average speed, and the two are rarely equal.
A trip that averages fifty is almost never done at a steady fifty. Traffic lights see to that. The average throws away everything that happened in between, which is what makes it easy to compute and dangerous to over-read.
Four trips. Rank them by average speed, largest first, by clicking them in order. Two of them tie, and the tie is the whole point.
3. Velocity: speed with a direction attached
Velocity is speed together with a direction. So a car can hold a perfectly steady speed and still have a changing velocity. All it has to do is turn.
“Constant speed” and “constant velocity” are not the same sentence. On a straight road they agree. On a bend they do not, and the bend is where the physics lives.
Steady speed, changing velocity
The car holds one speed the whole way round. Watch the two readouts. One of them never moves and the other never stops moving, and that contrast is the definition of velocity.
A passenger slides across the seat when the car rounds a bend even though the speedometer never moved. Nothing pushed them outward. They kept going the way they were already going while the car turned out from under them.
4. Acceleration is a bigger word than speeding up
Acceleration is how quickly velocity changes: speeding up, slowing down, or turning. It is not the same thing as going fast. A jet at cruising speed is not accelerating at all. A bicycle pulling away from a stop sign is.
5. A graph tells you its story through its shape
A graph of position against time answers the question before anyone measures anything. Flat means stopped. Straight and rising means going steadily away. Bending upward, more and more steeply, means speeding up. The steepness carries the speed; the shape carries the kind of motion.
Walk in front of the detector
Pick a way of walking. The figure walks it, and the graph draws itself as they go. This is the motion detector activity, with the graph appearing at the same moment the walking happens rather than afterward.
Two students produce graphs with the same shape but one walked faster. The faster walker’s line is steeper. What is the same is the shape: both straight, both sloping the same way.
Nobody can walk a vertical line. It would mean being in two places at the same instant, or covering ground in no time at all. That is not a limit on your legs. It is a limit on what a position can be.
Check yourself
1. A passenger walks toward the front of a moving bus. Who says the passenger is going faster, someone sitting on the bus or someone standing on the sidewalk? Explain in a sentence.
The person on the sidewalk. They see the walking added to the motion of the bus. The passenger on the bus sees only the walking. Neither is wrong, because they are answering with respect to different things, and neither of them said so out loud.
2. Four trips. A covers 100 km in 1 hour. B covers 100 km in 2 hours. C covers 50 km in 1 hour. D covers 200 km in 2 hours. Rank them by average speed and say which tie.
A and D tie for fastest at 100 km per hour, then B and C tie at 50. Ranking D above A because 200 is a bigger number is the mistake this question exists to catch: the per-hour part is the whole quantity.
3. A drive of 100 km takes exactly 2 hours. Must the car have been going exactly 50 km per hour at some moment? Argue for your answer.
Yes. The car starts at rest and averages 50, so its speed passed through 50 on the way up. Accept the argument rather than the word: a student who says “not necessarily” and defends it with a car that teleports has understood the logic, and the thing to push back on is the physical assumption, not the reasoning.
4. Rank by how much they are accelerating, most first: A a parked car; B a car on cruise control on a straight highway; C a car braking hard; D a car going steadily around a roundabout; E a dropped set of keys.
C and E are the largest, in either order with a reason, since the sizes are not given. Then D, which is accelerating despite its steady speed because the direction is turning. Then A and B, both zero. The two answers to watch for are putting B above zero because it is fast, and putting D at zero because the speed is steady.
Chapter 4, Newton’s Second Law. This chapter described the motion. The next one asks what causes it, and the answer turns out to be two things at once: the net force pushing it along, and the mass holding it back.