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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Which came first, movement or heat?

According to my measly understanding of the universe, when particles hit one another, some of their kinetic energy is transformed into heat. But when we heat particles (for instance, putting a bucket ...
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2answers
1k views

Rigid body dynamics joints

I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
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2answers
2k views

Help me get out of a speeding ticket

I was driving uphill from a complete stop for a distance of .4 miles estimated to take 1 minute in a navigation app. I was pulled over right after cresting the hill. The cop had me on radar going ...
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4answers
2k views

How can there be really any instantaneous velocity?

I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
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5answers
541 views

Intuitive answer to a kinematic problem

The problem: Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. ...
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4answers
532 views

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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5answers
387 views

Does an object move because it has Kinetic Energy or does it have Kinetic Energy because it is moving?

Maybe to explain I'm wondering if an object gains $\rm K.E.$ which causes it to have a velocity or does an object have a velocity which cause it to get $\rm K.E.$?
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8k views

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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2answers
137 views

Sign of acceleration

I'm developing an application using accelerometer sensor. I'm not good at physics so forgive me if the question is trivial. If I have 3 values of acceleration: $x$, $y$, $z$, I find acceleration ...
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1answer
7k views

Why is the velocity on the top of a wheel twice the velocity of its axle?

When a wheel is rolling, not skidding, and its axle moves at velocity $\vec{v}$, then a point on the top of its circumference will move at velocity $2\vec{v}$, shown below. I really don't ...
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2answers
872 views

Does a force really act on a body during a collision?

Consider two bodies A(black) and B(red) having equal mass. A is moving at a constant speed towards B, which is stationary. At certain point of time, they collide elastically, $\therefore u_{A}=v_{B}$ ...
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536 views

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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334 views

When can one write $a=v \cdot dv/dx$?

Referring to unidimensional motion, it is obvious that it doesn't always make sense to write the speed as a function of position. Seems to me that this is a necessary condition to derive formulas like:...
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215 views

Is $\dfrac{dx}{dt}$ a fraction or not?

I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that $\dfrac{dx}{dt}$ ...
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3answers
758 views

Does my (too low) tire pressure, affect the speedometer of my car?

Does my (too low) tire pressure, affect the speedometer of my car? How big is this effect?
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2answers
175 views

Does $y$-motion really have nothing to do with $x$-motion?

I am watching a Physics 1 for physical science majors on coursera.com, and in one of the concept tests there is a question that goes like this; "A bullet is fired horizontally from a rifle on the Moon ...
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2answers
6k views

Why do cars gain lift while going at a high speed?

I've been researching the physics involved with spoilers and I've just been turning up the same information about spoilers giving the back wheels of a car more traction by acting as an up side down ...
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2answers
45 views

Finding the Force of two objects - by using Acceleration but only ONE of the given masses?

I came across the following question in my physics textbook and wanted to try to solve it: A 1700 kg car is towing a larger vehicle with mass 2400 kg. The two vehicles accelerate uniformly from a ...
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2answers
433 views

Question on particle decay process, conservation of energy

Why is $$\Sigma^0 \rightarrow \Lambda +\pi^0$$ not a possible process? Charge and baryon number both are conserved. There's no issue with strangeness that I can tell. The masses in $\frac{Mev}{c^2}$ ...
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264 views

Work done on stationary rocket

Suppose I have a rocket thats exerts a force (with negligible loses in mass), which cancels out the downward force of gravity. Clearly my rocket could be moving at a constant velocity (ignore air ...
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2answers
172 views

How do the postulates of relativity relate Lorentz transforms to their inverses?

This question is about one of the assumptions involved when one is deriving the Lorentz transformation, for example under "Principle of Relativity" in Wikipedia's page on the derivations. Let me ...
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3answers
723 views

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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2answers
24 views

Why do the following two constant acceleration equations produce contradicting outputs?

Let acceleration = -a. I'm was originally trying to find the stopping distance in terms of $v_0$ and $a$ Two relevant equations of linear motion with constant acceleration then become $x = \frac12(-...
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505 views

Philae lander simulation off by factor of ~3

I'm trying to simulate the Philae landing by writing a program to compute the position of the lander vs time. According to various mission websites, the orbiter will match its orbit to the rotation of ...
4
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1answer
228 views

How to track the visual path of a LEO satellite as seen from the ground

I have been struggling with this problem for a while so I decided to ask. I'm new here and I'm not sure where this type of question belongs, so forgive me if this isn't the right section. I am ...
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Can these figures demonstrating the safety of “Archery Tag” arrows be correct?

There is a new sport called "Archery Tag" that involves shooting opponents with foam-tipped arrows fired out of a real bow. The official Archery Tag web site presents data that claims to show the ...
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641 views

Acceleration: A ball sliding down the inside of a semicircular bowl

Edit: To clarify, this is a homework question. But I couldn't care less about getting the answer to this specific question as it's not even assigned yet. It looks interesting and I want to understand ...
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494 views

Best shape to reduce the splash of a droplet?

Our coffee machine catches the last couple of droplets, after your cup is removed on a shape to reduce plash of the coffee droplets. These shapes are placed inside the spill reservoir. The shape ...
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3answers
6k views

What is displacement? Position relative to a reference point or change of position

What is the "official" or most useful definition of displacement in the context of kinematics? There are two common ones: Displacement is the length and direction of a line from a fixed reference ...
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1answer
29 views

Transformations and kinetic energy

From the equation $E_k=\frac12mv^2$ you can determine more energy is necessary to accelerate a mass the higher your initial velocity is. For example, three times more energy is necessary to accelerate ...
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1answer
454 views

Lorentz-invariant phase space of a three-body decay process

I am not following the use of delta function in the 3-body decay process. In $\gamma^* \to gq\bar{q}$ process, with $\gamma^*$ being a virtual photon, we have a phase space factor $$d^9R_3 = \frac{d^...
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9answers
938 views

Can velocity be an undefined quantity?

We have the image below displaying the uniform velocity by time-distance graph. At every point velocity is constant but what if distance and time both become zero as at origin in the graph is? The ...
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2answers
1k views

How can an object move from point A to point B?

If I was at point $A$ and I wanted to walk directly to point $B$, I would have to walk half way to point $B$, but before that I would have to walk half way to halfway to halfway to point $B$ and half ...
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4answers
859 views

What causes a car's velocity to follow the front wheels' direction?

I'm trying to simulate a car with correct physics models. In this example we let the car have a constant speed, and there are no forces (friction and drag) to slow down the speed. Here's a video that ...
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3answers
2k views

Free falling objects

My teacher and I are in the middle of an argument because she says that if you were to drop two objects at the same time and the same height, but with different initial velocities, both of them would ...
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3answers
9k views

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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2answers
769 views

How much does it cost every time your car stops for a traffic light?

Every time we have to stop the car, it is costing us extra money, because we have to then accelerate to full speed again. I would like to know how much. In order to simplify the situation, we can ...
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1answer
811 views

Two vehicles moving in a line with different accelerations

Let two similar vehicles starting at rest in a straight line (with a distance of $D$ between them) have time-varying accelerations in the same direction. If both of them have similar time varying ...
3
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1answer
143 views

How is $ \frac{dv}{ dt} = a $?

I know how , in the physical sense - $$\frac {dv}{dt} = a$$ But, even after thinking a lot, I am not able to see the fault in this - $$\frac {dv}{dt} = \frac {d(st^{-1})}{dt} = \frac {sd(t^{-1})}...
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1answer
111 views

Contradiction of a scalar product

Can anyone resolve this contradiction: $$\vec{r}\cdot\dot{\vec{r}}=\frac{1}{2}\frac{d}{dt}\left(\vec{r}^2\right)=\frac{1}{2}\frac{d}{dt}\left(\left|\vec{r}\right|^2\right)\equiv\frac{1}{2}\frac{d}{dt}...
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4answers
8k views

Maximum range of a projectile launched from elevation “dumbed down”

I am trying to conceptually understand why the angle which produces the greatest range for a projectile launched with an elevation is not 45 degrees. I have exausted all other options, and I hope that ...
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6answers
7k views

Ion Drive Propulsion Top Speed

I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at ...
3
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1answer
348 views

Calculating Kryptonian speed in the movie “Man of Steel”

This is my first question, so I'm not sure if this is the right place to ask but: How would you go about calculating the speed of Kryptonians in the movie Man of Steel (2013)? Specifically, I'm ...
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4answers
2k views

How to calculate a collision which is partly elastic and partly inelastic?

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision). ...
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2answers
17k views

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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633 views

The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available

If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
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1answer
242 views

Is it possible to rotate an angle on perfectly smooth ice?

You must start and end with the same pose. Prove it if you think you can't.
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3answers
242 views

Object docking in Space

How do objects dock in space? There's a recent piece of news that Keppler would dock to the ISS sometime this week. I want to know the operational aspects of it - considering the velocity of the ...
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3answers
2k views

Distance travelled in free-fall

When an object is in free fall, we have: $a(t) = g - \frac{c}{m}v(t)^2$ where $g$ is acceleration due to gravity, $m$ is the mass of the object, and $c$ is the coefficient of air resistance. How ...
3
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1answer
409 views

$v^2 = 2ax$ or $v^2 = ax$?

As far as I am aware, $v^2 = 2ax$ is the formula to find the velocity in various questions. If kinetic energy = work, $$\frac{1}{2}mv^2=Fx$$ $$mv^2=2max$$ $$v^2=2ax$$ We use this formula to solve ...