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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What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?

Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties: For a ...
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Area under a displacement graph

If the area under an acceleration-time graph denotes velocity and the area under a velocity-time graph denotes displacement, what exactly does the area under a displacement-time graph denote?
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Why do far away objects appear to move slowly in comparison to nearby objects?

When we are in a moving train, nearby stationary objects appear to go backwards. In Physics, relative velocity can be employed to explain the phenomenon: velocity of object w.r.t train = velocity ...
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Physics of simple collisions

I'm building a physics simulator for a graphics course, and so far I have it implementing gravitational and Coulomb forces. I want to add collisions next, but I'm not exactly sure how to go about ...
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Do free particles slow down in expanding universe?

My favorite toy model of cosmic microwave background in the expanding universe is a cube with totally reflective walls. If CMB is a black-body radiation, it must be isotropic and homogeneous - the ...
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Newton's second law: system with three blocks and a pulley

Here's a common Newtonian mechanics problem. What horizontal force must be applied to a large block of mass $M$ shown in the figure so that the blocks of mass $m_1$ and $m_2$ remain stationary ...
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How does this magnetic toy work?

A nephew of mine has this toy called "Gravitrax". It is basically a track building kit - you can build various tracks for iron balls which go through the track thanks to gravity. However, there is ...
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Why does a stream of water behave like this when aimed against a spoon or into a glass?

I noticed while doing everything except the dishes that water behaves quite strange. These two things might be two different phenomenon, but the water acts in a similar way in both cases. Spoon and ...
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Should acceleration be included in state vector of a Kalman filter?

I'm developing (actually adopting existing solution) a Kalman filter to model motion of a vehicle (UAV or automobile). The state vector will include position, velocity, and, possibly, acceleration. ...
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Is acceleration continuous? [duplicate]

The extrapolation of this Phys.SE post. It's obvious to me that velocity can't be discontinuous, as nothing can have infinite acceleration. And it seems pretty likely that acceleration can't be ...
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Can an object reverse its direction of acceleration even though it continues to move in the same direction?

Can anyone please explain me on this matter along with day to day examples?
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Question about derivation of kinematics equations

Apologies if this has been asked before, but I browsed the sub and couldn't find something specific. I understand the derivation for one of the equations as follows: \begin{gather} \frac{dv}{dt} = a ...
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Why do we equate an indefinite integral to a specific value?

Suppose we want to obtain a displacement vector defined as $\mathbf s(t) = x(t)\mathbf i + y(t)\mathbf j + z(t)\mathbf k$ from the components of a velocity vector $\mathbf v(t) = \dot x(t)\mathbf i + \...
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If an object moved 5 meters in a second, how can its velocity be 10 m/s? [duplicate]

On physicsclassroom.com, an assignment gives data for an object experiencing acceleration: This is the corresponding chart for the object's velocity: At $0$ seconds the position of the object is $0$...
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Ball thrown from a moving train

This is not a question about throwing a ball vertically in a moving train. I am asking what would happen if I throw a ball in a horizontally in a moving train. Assume I am facing an exit door of a ...
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Can a free particle ever emit a particle?

I have found this question here Can a free particle absorb/emit photons?, along with other resources that show a free particle cannot emit a photon (in a vacuum). Now, I am 90% sure it does, but ...
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Why is average velocity the midpoint of initial and final velocity under constant acceleration?

Since average velocity is defined as$^1$ $$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$ where $\vec{\mathbf x}$ denotes position, why is this quantity equal to $$\...
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Is running in a zigzag helpful in avoiding being shot by an arrow? [closed]

Two people A and B start at a certain point. B runs away from A to another point. A shoots arrows at B. Is it helpful for A to run in a zigzag rather than in a constant direction? To be more precise:...
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Somewhat unusual projectile motion question

A stone must fly over two walls of height $h_1$ and $h_2$ $(h_2~ > ~h_1)$ from the side of the lower wall. The distance between the upper points of the two walls near which the stone's trajectory ...
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How to tell if the collision is elastic or inelastic?

I'm a programmer and a game developer, not a mathematician or a physicist. So please go easy on the math :) I know two things: How to find the new velocities of two objects after an elastic ...
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Intuitive logic behind this beautiful result of successive time of collisions of two bodies

INPhO 2017 Problem 3 Two identical blocks A and B each of mass $M$ are placed on a long inclined plane (angle of inclination = $\theta$) with A higher up than B. The coefficients of friction ...
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View from a helicopter rotor: why is the horizon distorted?

This video ("rotor panorama") was captured by a camera attached to the rotor head of a radio-controlled helicopter, with the frame rate set to the rotor's frequency. During a long segment of the video,...
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Is there a scalar acceleration?

Distance is paired with Displacement and it seems to be a bigger idea than just the magnitude of Displacement. Speed is paired with Velocity. I have always thought that there is not such pairing with ...
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Is Torricelli's law “wrong” for big holes? - Tank draining problem

Consider a tank full of water with a constant cross-sectional area A1 placed vertically on the ground. Now someone drills a hole of an area A2 in the bottom of the tank, and the liquid starts escaping ...
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How to calculate the kinetic energy of supernova ejecta?

I believed I could use $0.5\times M_{ej} V_{ej}^2$, with $M_{ej}$ being the ejected mass and $V_{ej}$ being the velocity of the ejected mass. But I noticed in this and this that the the mean velocity ...
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Why the round trip instead collision time?

From Newton's second law, the $\Delta t$ is defined as the collision time, but why in this case, it can be assumed to be the value of time between successive collisions on 1 wall? If I have an ...
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Why does a perpendicular force not change speed?

I have been taught that a perpendicular force acting on an object will only change the direction of its velocity, not its magnitude. The explanation that was provided to me is that because there no ...
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Is there a 2D generalization of the coefficient of restitution?

The coefficient of restitution characterizes a collision in one dimension by relating the initial and final speeds of the particles involved, $$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$ In a ...
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Why do office chairs rotate when pushed/pulled out?

A common source of frustration when I'm at work is the fact that my rolling office chair's wheels rotate whenever I push it forward or backward from my desk, which can cause it to bump my computer ...
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Does entropy apply to Newton's First Law or does “acted upon” always require an external factor?

First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, ...
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A dumbbell rolls down a slope, what happens when it touches the ground?

As in the title, our Physics teacher gave us this brain teaser after learning introductory motion. "If I have a dumbbell [with bigger weights than handle] that is rolling down an incline with only ...
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Why doesn't the relativistic formula for momentum appear consistent with collisions?

The relativistic formula for momentum is $$p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}} \,.$$ In the following example, I apply the formula in the most basic way possible to the addition of velocities. ...
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Is there mechanical strain on a wire along the direction of current flow?

The (attractive) magnetic force on two parallel wires can be seen by the two wires bending towards each other. This can be explained by the Lorentz force acting on the charges and the charges "pulling"...
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Two formulas for a particle's acceleration

While on a class my teacher was taking about particle's motion in space. At some point she said the following: Consider that the particle's path is described by a curve in space defined by the ...
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Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
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What is “kinematic inversion” (from geophysics) in mathematical terms?

I am a mathematician working on a seismic imaging problem, and am currently (attempting to) read some geophysics papers (this one (Ruiz, Madariaga 2011) and this one (Di Carli, Francois-Holden, Peyrat,...
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Why isn't average speed defined as the magnitude of average velocity?

Speed is usually defined as the magnitude of (instantaneous) velocity. So one could assume that average speed would be defined as the magnitude of average velocity. But instead it is defined as $$s_{...
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How does instantaneous velocity or acceleration have any other numerical value than 0? [duplicate]

Instantaneous velocity is defined as the limit of average velocity as the time interval ∆t becomes infinitesimally small. Average velocity is defined as the change in position divided by the time ...
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Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light?

I have found these two formulas: $v = at + v_0$ $x = \frac{1}{2}at^2 + v_0t + x_0$ a is the acceleration v is the velocity x is the position t is the time $v_0$ is the initial velocity $x_0$ is the ...
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How does an object's motion behave if dropped from an aeroplane travelling diagonally upwards?

Imagine an aeroplane travelling with velocity $v$ at some angle $\alpha$ from East to North. A box is dropped from the aeroplane. What would the projectile of the box be? Would it be a parabola with ...
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Is there any such thing as a change in acceleration (ex: 3 m/s/s/s)? [duplicate]

If there exists something like that, then in $distance/time/time/time$, how is it expressed?
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Why does acceleration need to be constant if integrating?

My teacher wrote the following: Constant Acceleration If acceleration is constant, then: $$\vec{v}(t) = \int_0^t \vec{a}(t')dt'\ + \vec{v_0}$$ and $$\vec{x}(t) = \int_0^t \vec{v}(t')dt'\ + \vec{...
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Why the photon can't produce electron and positron in space or in vacuum?

$$\frac{hc}{\lambda} = K_e + K_p + 2m_e c^2$$ could be the energy conservation equation for a photon of wavelength $\lambda$ decaying into a electron and positron with kinetic energies $K_e$ and $K_p$ ...
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Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion

The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is ...
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In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter? [duplicate]

Assume a point-mass $m$ is travelling in a straight line, and a force $F$ will act on $m$ (in the same direction as $m$'s velocity) over a constant distance $d$; why doesn't $m$'s velocity matter to ...
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Dodging paintballs

I was recently watching The Matrix, and was considering the speed at which one needs to move to literally dodge a projectile. Now, in real life, it is impossible to dodge bullets as such a feat would ...
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Has a body angular momentum and torque only in a circular path?

In different contexts, my book(Principles of Physics by Resnick, Halliday ,Walker) , they wrote For torque, the path need no longer be a circle and we must write the torque as a vector $\vec{\tau}$...
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If an electric car were to drive without having to stop, would the range be greatly affected by the speed at which the vehicle is moving?

Of course aerodynamics factors into this question, and the faster you are moving the more air you have to push out of your way, the more energy you use. But would the difference be only a small ...
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Why does light travel at the same speed when measured by a moving observer? [duplicate]

I know the hypothesis that the light speed is constant is retained by experiments. But is there any theory explaining why the light speed is constant no matter how an observer moves relative to light? ...
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Newton's First Law of Motion; Empirical Aspects

Newton's first law states that in an inertial frame, a body at rest continues to be at rest, and a body in constant rectilinear motion continues its motion, unless an external force is applied upon ...

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