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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How long does it take to optimally change position and velocity?

A spaceship moving in two dimensions is at position $(x, y)$ and has a velocity $(v_x, v_y)$. It also has a maximum acceleration $a_{max}$. Its goal is to be at position $(x', y')$ with a velocity of ...
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2answers
1k views

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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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 ...
4
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2answers
1k 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
875 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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2answers
5k views

How can an object's instantaneous speed be zero and it's instantaneous acceleration be nonzero?

I'm studying for my upcoming physics course and ran across this concept - I'd love an explanation.
4
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3answers
557 views

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? ...
4
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2answers
523 views

Does a force act on the body during 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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2answers
120 views

The velocity of a cloud?

I noticed an unusually fast moving cloud this morning. My questions: What is the average velocity of a cloud on Earth? What is the greatest ever recorded cloud velocity? What factors affect the ...
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3answers
210 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 ...
4
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2answers
144 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 ...
4
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2answers
159 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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1answer
345 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
votes
1answer
135 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 ...
4
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2answers
679 views

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 ...
4
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2answers
290 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 ...
3
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2answers
1k views

Proof of centripetal acceleration formula ($a_c = \frac{v^2}{r}$) 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 ...
3
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1answer
95 views

Contradiction of a scalar product

Can anyone resolve this contradiction: ...
3
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1answer
2k 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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3answers
5k 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 ...
3
votes
2answers
108 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 ...
3
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2answers
3k 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
433 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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3answers
733 views

Physical Variables of Circular Motion

To me, the definitions of variables involved in circular motion are rather confusing (perhaps due to the lack of understanding on my part), hence the question. As I understand it, there are two ...
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6answers
5k 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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2answers
375 views

Is the speed of a person falling down different if doing a forward somersault during the fall?

Let's imagine this in an situation where a person jumps down from a smaller building, a garage for example. The exact numbers aren't really important here, since I'm not aiming for an exact answer, ...
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3answers
225 views

A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]

I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was ...
3
votes
1answer
285 views

How deep is the well, given this data?

A rock is dropped into a well. A timer starts when the rock is dropped and is stopped when the noise of the rock hitting the ground of the well is heard. How deep is the well? Here's what I have so ...
3
votes
1answer
583 views

What is the longest distance that can be jumped after swinging from a rope?

In the movie Mission Impossible 3, the main character Ethan Hunt tries to enter a building in Shanghai by swing through the sky, as shown below: The jump consists of 2 sections, the red part, which ...
3
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1answer
40k views

Solving for initial velocity required to launch a projectile to a given destination at a different height

I need to calculate the initial velocity required to launch a projectile at a given angle from point A to point B. The only force acting on the projectile after launch will be gravity – zero air ...
3
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2answers
118 views

Why and when do we differentiate or integrate equations in physics? [closed]

I'm an engineering student and none of my professors ever explained why do we use derivations and/or integrations in physics. So I have this task, it goes like: The object is moving in a positive ...
3
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3answers
77 views

The motion of the particle satisfies $\textbf{v} = \textbf{c}\times \textbf{r}$

Why does a particle with position $\textbf r(t)$ that satisfies $\textbf{v}(t) = \textbf{c}\times \textbf{r}(t)$ follow a circle that lies in a plane perpendicular to $\textbf{c}$ with centre on a ...
3
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1answer
3k views

How do kinetic energy and linear momentum relate?

It took me quite a long time to click my gears in place and even then I'm not sure it's completely correct. The problem is that I need to understand these concepts (physics concepts; not just these ...
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3answers
593 views

A freefalling body problem, only partial distance and time known

Well, I've been trying to figure out a problem which I imposed on myself, so no literal values included. Unfortunately, my brain is not cooperating. The problem states: What is the height from ...
3
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1answer
63 views

Non-deterministic particle system

This question is in the spirit of Norton's dome, an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the Picard–Lindelöf theorem guarantees the ...
3
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2answers
627 views

A block on a wedge

The system is as follows - Friction exists only between the 2 blocks. I am trying to find out the accelerations of $m_1$ and $m_2$. Let $a_2$ be acceleration of $m_2$, and $a_x$ and $a_y$ be the ...
3
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3answers
5k views

Angles on swing sets

I'm building a swing set for my children. All of the designs I've seen involve building two A-frames and connecting them at the top with a crossbar/beam from which hang the swings. The A-frames are ...
3
votes
1answer
210 views

A practical deceleration question

My friend is a U.S. Army paratrooper. Today, through an unfortunate series of events, he was jerked out of a C-17 traveling at 160 knots by his reserve parachute. First-hand accounts describe it as he ...
3
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2answers
483 views

Oscillation of a rolling sphere in a bowl [closed]

This is a homework task. I already came to a result but I am very unsure. The task: In a bowl with the shape of a semi-circle ($R$ = 0.5m) a sphere (there is no specification for the size of the ...
3
votes
3answers
617 views

How do I meaningfully divide by a vector?

How long does it take a baseball with velocity $(30, 20, 25) m/s$ to travel from location $r_1 = (3, 7,−9) m$ to location $r_2 = (18, 17, 3.5)m$? I am thinking that it should be the ...
3
votes
1answer
106 views

Galaxy Kinematic Fitting: How to deal with Point Spread Function (PSF)

The past few months I have been studying astronomy and Integral Field Spectroscopy (IFS). What I want to do is to fit a galaxy kinematic model to data (ie: estimate the model parameters that give the ...
3
votes
2answers
171 views

Rotational velocity of face-on spiral galaxies using spectroscopy

I am doing my first steps in spectroscopy (IFS actually) and how we can learn more about galaxies by using it. I came up with a simple question which, unfortunately, I can not answer: How can we ...
3
votes
2answers
649 views

Is a heavier skier faster? [duplicate]

Is it true that a heavier skier goes faster? If it is, why is that? My intuition would be that the speed gained by a skier should be independent from its mass, since both its acceleration and the ...
3
votes
1answer
472 views

How do I find the initial velocity in this problem?

An X-ray tube gives electrons constant acceleration over a distance of $20\text{ cm}$. If their final speed is $2.0\times 10^7\text{ m/s}$, what are the electrons' acceleration? I know this ...
3
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2answers
214 views

Find distance between turtles

I've been thinking about the following problem for some time now and was wondering if anyone could shed any light on it. At time $t = 0$, turtle A sits at ...
3
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1answer
472 views

Lab observation correct? As distance decreases, velocity increases, stderr decreases

The experiment goes like this: Allow a moving cart to move from the top of an incline plane ($x_0$) downwards. The time taken will be recorded by the picket fence (those things you see wired up). ...
3
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2answers
1k views

Formulas for ball rolling in a bowl?

I'm developing a program where I've a ball/sphere rolling in a bowl from the side at top, till the center at bottom, and I'm trying to get the formulas for: The rotation angle and the position of ...
3
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0answers
40 views

Does a tire need to slip to generate force?

Recently, I have been doing some research on racing and tire modelling. While I was doing this, I encountered many curves like those shown below. While I understand the need of slip angles to ...
3
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1answer
120 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 ...
3
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1answer
111 views

How to interpret $t^2$? [closed]

I can't think of the meaning of squaring the Time (multiplying it by itself). It makes sense in Mathematics. But how can you figure it out in nature (or physics). As an example, the formula ...