Common questions students raise while working through Chapter 2. Each answer is short and direct; links point to the relevant section for deeper reading.
1) What's the difference between displacement and distance?
Displacement (Δx) depends only on start and end positions — it can be positive, negative, or zero. Distance is the total path length — always positive. If you return to your starting point via a round trip, Δx = 0 but distance is nonzero. §2.1
2) If instantaneous velocity is meaningful at t = 0, how can there be motion "at an instant" with no time elapsed?
Instantaneous velocity is not "distance divided by zero time" — it's an instantaneous rate of change. Like a heart rate: right now it's 70 beats per minute even though no minute has passed. Mathematically it's a limit, physically it's what nature actually determines. §2.2
3) Does "negative acceleration" mean "slowing down"?
Not necessarily. Negative acceleration means acceleration in the negative direction of the axis — nothing else. If the object is moving in the negative direction, negative acceleration is speeding it up, not slowing it down. See the 4-case table. §2.3
4) At the peak of a throw, acceleration is zero because velocity is zero — right?
No. At the peak, instantaneous velocity is zero, but acceleration is still -g. If acceleration were also zero, the ball would hang in the air — but it immediately starts falling, so there's acceleration. §2.5
5) Why do all objects fall with the same acceleration — a light feather and a dense stone?
From F = ma (Newton 2) and F = mg (weight), mass m cancels and a = g remains. For every object. Air resistance adds something extra — a light feather quickly reaches terminal velocity because drag is large relative to gravity. In vacuum (like on the Moon), feather and hammer land simultaneously. §2.5
6) How do I know which kinematic equation to use?
Of the five quantities {x_0, v_0, v, a, t}, usually 3 are known and 2 are unknown (one target, one missing). Pick the equation that omits the missing variable. See the §2.4 table. §2.4
7) What if acceleration is not constant — do the §2.4 equations fail?
Yes. Go back to primary definitions: v = ∫a dt, x = ∫v dt — that is, integrate. Or use graphical analysis (area under the curve). §2.6
8) Why does stopping distance scale with velocity squared, not linearly?
From equation 3: v² = v_0² - 2|a| x_stop (when v = 0). Solve: x_stop = v_0² / (2|a|). The v_0² says doubling speed needs four times the distance. A driving fact that becomes critical on wet or foggy roads. §2.4
9) If a car goes from a positive speed to zero, is its acceleration negative?
Depends on convention. If positive axis points in the direction of motion, yes a < 0. If positive axis points backward, a > 0. The physics doesn't change — only the signs. What matters is being consistent with your chosen convention. §2.3
10) Why is average velocity the mean of initial and final velocities under constant acceleration?
Because velocity varies linearly with time (from v = v_0 + at). The average of a linear function over an interval is the value at the midpoint. This doesn't work for nonlinear motion. §2.4
11) In the real world with air resistance, what is terminal velocity?
When drag force (upward) equals gravity (downward), net acceleration goes to zero — and the object falls at a constant (terminal) velocity. For a skydiver, about 55 m/s ≈ 200 km/h. For a paper feather, maybe 0.5 m/s. Depends on the drag-to-weight ratio. §2.5
12) Is g = 9.8 m/s² always right?
No — it's a surface approximation. At the Everest summit ~9.78, in the ISS ~8.7, on the Moon ~1.62. It depends on the distance from the gravitating body's center: g = GM/r². Gravity Article 3
13) Are ISS astronauts truly "weightless" — meaning zero gravity?
No. g at the ISS is about 88% of surface gravity. They appear weightless because they are in free fall — the station is continuously falling toward Earth, but its horizontal motion is fast enough that it keeps missing the surface. That's an "orbit". Both astronaut and station accelerate at the same rate (equivalence principle). Gravity Article 3
14) Second derivative of position = acceleration — is this the same acceleration we "feel" in a car?
Yes. Every time you feel "pressed into the seat", that's your physical acceleration. 9.8 m/s² = 1 g = normal weight on Earth. Ordinary driving is a fraction of g, a sports car close to 1g, a fighter jet 9g or more. What you sense is the second derivative of position. §2.3
15) Are the kinematic equations valid at all speeds?
No — only for speeds far below the speed of light. At v ≪ c, Newton's formulas are extremely accurate (error ~(v/c)²). When velocities approach the speed of light, you must use special relativity (Einstein). For instance, v cannot exceed c ≈ 3 × 10⁸ m/s. In everyday physics (up to hundreds of km/s), we see no discrepancy.
16) If two objects are released from the same height — one dropped and one thrown horizontally — which lands first?
They land at the same time. The horizontal component of velocity has no effect on the vertical fall — vertical motion is independent. One of Galileo's beautiful discoveries. This is a Chapter 4 topic (2D motion).
17) In "ball dropped from the window of a moving train", where does the ball land?
From an observer inside the train: the ball falls straight down. From an observer on the ground: the ball traces a parabola — because at release, it retained the train's horizontal velocity (superposition principle). Also Chapter 4.
18) Which tools from Chapter 2 will I need later?
All of them. Differentiation (instantaneous velocity) and integration (displacement from velocity) show up in every subsequent chapter. The constant-acceleration equations (§2.4) appear repeatedly in Chapter 4 (projectiles), Chapter 5 (dynamics), Chapter 6 (friction), even Chapter 15 (gravitation). If these aren't fluent, the rest of Halliday gets hard.
19) If I only have time for the most important parts of Chapter 2, which sections?
No question: §2.4 (four kinematic equations) and §2.5 (free fall). Together they solve 90% of practical problems. If you have even less time, learn just those two. The rest is theoretical background that keeps you from making mistakes. §2.4 §2.5
20) In the §2.8 exercises, how do I know if my answer is right?
- Check units: if your answer is a length but you got a time (or unit-less), something's wrong
- Check magnitude: if a human's velocity exceeds the speed of light, wrong
- Check sign: if a falling ball has positive velocity (with axis up positive), wrong sign
- Check limits: test your formula at edge cases (
t = 0,a = 0,v_0 = 0— each should give a sensible answer)
Chapter 2 wrap-up
Three main ideas to take away:
- Kinematics is the language of motion description. Without saying "why", it precisely captures "how".
- Position, velocity, acceleration — all three chain together via differentiation. The tools: differential and integral calculus.
- Constant-acceleration equations — four equations that solve 90% of practical problems. Only when
a = const.
Next chapter: vectors — because in the real world, motion is more than 1D. We need to learn how to handle direction-carrying quantities.
🎓 You've finished Chapter 2! If there's a question you think should be here but isn't, let us know.
Have a question? 🤔
If something isn't clear or you have a question, ask it here. The answer will be published on this page.