# Questions tagged [kinematics]

The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.

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### Why does kinetic energy increase quadratically, not linearly, with speed?

As Wikipedia says: [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$. Why does this not increase linearly with speed? Why does it take so ...
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### Does a thrown ball have kinetic energy at the top of the curve?

I'm going through physics with my 5th grade child. There is a question and answer that indicates that a airborne ball at the top of the trajectory does not have kinetic energy. The diagram below ...
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### What is the difference between “kinematics” and “dynamics”?

I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics". I first encountered this in Jackson's E&M book, where, in ...
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### Why doesn't a braking car move backwards?

The net force on an object is equal to the mass times the acceleration, $F = ma$ When I brake on a (moving) car, the net force is negative, therefore causing the resulting acceleration to also be ...
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### How effective is speeding?

At a simple level, speeding in a car attempts to minimize the time required to travel a distance by utilizing the basic relationship: $$d=st$$ So for a given distance, time should be inversely ...
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### How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
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### Why is 7 TeV considered as a big amount of energy?

Considering that $7$ TeV is more or less the same kinetic energy as a mosquito flying, why is it considered to be a great amount of energy at the LHC? I mean, a giant particle accelerator that can ...
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What kind of motion would a (preferably dimensionless for simplicity) body do if the force acted on it was proportional to the semi-derivative of displacement, i.e. $$m \frac{\mathrm{d}^2 x}{\mathrm{... 4answers 13k views ### Why do most office chairs have 5 wheels? (Inspired by Why are four legged chairs so common?) I've been wondering for a while... Why do most wheeled office chairs have 5 wheels? My guess would be that while stability vs. simplicity results ... 5answers 7k views ### How does a mobile phone vibrate without any external force? How does a mobile phone vibrate without any external force? By Newton's law, any body can't move without any external force 7answers 126k views ### Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph? I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ... 4answers 6k views ### With what velocity are we moving along the time dimension? Does the question make sense? Velocity along time axis means v_t=\mathrm dt/\mathrm dt? If it doesn't, please explain where the flaw is. Taking time as measure like length? Or do we need to ... 13answers 64k views ### Recommendations for good Newtonian mechanics and kinematics books What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.? 7answers 18k views ### How can kinetic energy be proportional to the square of velocity, when velocity is relative? Let's start with kinetic energy (from los Wikipedias) The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a ... 6answers 8k views ### Can an object *immediately* start moving at a high velocity? What I mean is, suppose a ball is fired from a cannon. Suppose the ball is moving at 100 m/s in the first second. Would the ball have started from 1m/s to 2m/s and gradually arrived at 100m/s? And is ... 5answers 18k views ### Why does the sun make me feel warm? For a while I thought that the reason I felt warmth from the sun was because my skin was being hit by photons, but then I realized that photons also hit me when I take an X-ray, but I don't feel any ... 1answer 1k views ### Modelling the movement and jumps of a chalk while drawing a dashed line on a blackboard You probably know that if you try to draw a line using a piece of chalk on a blackboard , under some conditions (for example, \alpha<\frac{\pi}{2} in the picture below) you will have a dashed ... 8answers 69k views ### Inertia Vs Momentum At my recent lesson on kinematics, my teacher taught about inertia and momentum. This is what she said. Inertia: a characteristic of an object that resists changes to its state of motion. Momentum: ... 9answers 6k views ### The instant an accelerating object has zero speed, is it speeding up, slowing down, or neither? This problem is from Khan Academy. Specifically for the blue point circled in red, the answer is that at this blue point, the object is neither speeding up nor slowing down. When I think about the ... 7answers 4k views ### What's the difference between average velocity and instantaneous velocity? Suppose the distance x varies with time as:$$x = 490t^2.$$We have to calculate the velocity at t = 10\ \mathrm s. My question is that why can't we just put t = 10 in the equation$$x = 490t^2$... 3answers 1k views ### Why there is a$\frac{1}{2}$in the distance formula$d=\frac{1}{2}at^2$? I'm preparing for my exam, but I have difficulties in perceiving why there is a$\frac{1}{2}$in the distance formula$d=\frac{1}{2}at^2$? 6answers 10k views ### Zero velocity, zero acceleration? In one dimension, the acceleration of a particle can be written as: $$a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt} = v \frac{dv}{dx}$$ Does this equation imply that if: $$v = 0$$ Then, $$\... 5answers 553 views ### Does the mass point move? There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at t=0 its position is 0, i.e., ... 1answer 1k views ### Non-uniform Circular motion velocity optimization Consider the following problem: A vehicle (modeled as a particle) enters into a circular arc trajectory at point s_1 (given), see figure below. If at s_2 the speed of the vehicle is not to ... 4answers 92k views ### Why does a ball bounce lower? If a ball hits the floor after an acceleration then why does it bounces lower? I mean the Energy is passed to the floor then why does the floor give back less Energy? 3answers 3k views ### How does anything move? [duplicate] So in order for two things A and B to move apart, for example, relative to each other, B can be set into motion away from A. This means that we have to increase B's velocity and therefore ... 5answers 30k views ### Why does work equal force times distance? [duplicate] My book says: Energy is the capacity to do work and work is the product of net force and the 1-dimensional distance it made a body travel while constantly affecting it. This seems quite ... 5answers 99k views ### How to get distance when acceleration is not constant? I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ... 5answers 6k views ### How to brake 'beautifully'? Sometimes when I'm driving my car, I play a "game" against myself in which I try to minimize the deceleration felt by passengers (including myself) while still braking in a reasonable short space. I ... 2answers 51k views ### Difference between momentum and kinetic energy From a mathematical point of view it seems to be clear what's the difference between momentum and mv and kinetic energy \frac{1}{2} m v^2. Now my problem is the following: Suppose you want to ... 4answers 41k views ### What stops giant cruise ships toppling over in rough seas? A week ago, 2 of the most gigantic cruise ships in the world docked near my city. If you have seen one, or been on one, you will know how large they are. They look extremely unsafe to me, although ... 7answers 9k views ### Flat throw vs 45 degree throw of a ball Why does my sports coach tell me that when I'm fielding I should throw the baseball 'flat' to get the maximum distance? I thought from physics that you get the most distance from throwing at a 45 ... 3answers 5k views ### Center-of-mass frame for massless particles Given a scattering event where a photon and electron go in and a photon and electron come out, what is the center of mass frame? I'd say, since the photon has no mass, it's the rest frame of the ... 5answers 14k views ### Why are objects at rest in motion through spacetime at the speed of light? I read that an object at rest has such a stupendous amount of energy, E=mc^2 because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ... 5answers 2k views ### What is the best path for a given initial and final state? I am trying to calculate an efficient acceleration curve given starting and final positions and velocities. I'm assuming no friction, and that the acceleration can be applied in any direction at any ... 3answers 3k views ### Why collide a moving particle with a particle at rest, rather than two moving particles? I was just reading some lecture notes about relativistic and quantum mechanics, and in the later part of this page the author demonstrates that any relativistic particle collision in the "lab" ... 3answers 8k views ### Is it possible to have a rate of change of acceleration? I know this may seem a weird question, but it always bothers me. My physics book (Resnick,Halliday,Walker), and also various sites never say anything beyond acceleration. But when a moving body is ... 4answers 280 views ### Problems in the relation a=v\frac{\mathrm{d}v}{\mathrm{d}x} We all know a = \frac{\mathrm{d}v}{\mathrm{d}t}. A little application of the chain rule leads to the relation$$a=v\frac{\mathrm{d}v}{\mathrm{d}x}$$But the above equation shows that a=0 whenever ... 4answers 3k views ### How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true? Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ... 5answers 1k views ### Infinite series of derivatives of position when starting from rest Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ... 3answers 926 views ### Is acceleration an average? Background I'm new to physics and math. I stopped studying both of them in high-school, and I wish I hadn't. I'm pursuing study in both topics for personal interest. Today, I'm learning about ... 1answer 339 views ### Is there an explicit connection between rolling-shutter images of rotating propellers and interference patterns with optical vortices? The rolling shutter effect is a neat fact of the geometry of modern CCD cameras and how they interact with objects that move faster than the camera can handle, and it's been beautifully explained by a ... 5answers 48k views ### Why there is a 1/2 in kinetic energy formula? [duplicate] Possible Duplicate: Why is there a \frac 1 2 in \frac 1 2 mv^2? Hèllo, I have a question about kinetic energy formula. As you know, in kinetic energy formula, we have: \large\frac{1}{2}mv^... 4answers 3k views ### What would qualify as a deceleration rather than an acceleration if speed is unchanged? The instantaneous acceleration \textbf{a}(t) of a particle is defined as the rate of change of its instantaneous velocity \textbf{v}(t):$$\textbf{a}(t)=\frac{\mathrm{d}}{\mathrm{d}t}\textbf{v}(t).... 7answers 1k views ### Can we divide a vector by another vector? How about this:$a = vdv/dx?\$

My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$ It says acceleration vector equals velocity (as ...
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### Static Friction - Only thing that can accelerate a train?

I'm a computer programmer that never studied physics in school and now it's coming back to bite me a bit in some of the stuff I'm being asked to program. I'm trying to self study some physics and I'...
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### In an electron-positron annihilation, in what direction are the photons released?

I read that, in an electron-positron annihilation, at least 2 photons are produced, because of the law of conservation of momentum. my question is: in what direction are those photons released? and ...
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### Can one rise through a free-falling rope?

I am a little confused about this question. I cannot imagine that it is possible to rise through a rope (assuming inextensible) that isn't fixed in its upper end. But when I solve this problem, I see ...