# Questions tagged [kinematics]

For questions on the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

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### Finding the velocity potential of liquid between two concentric sphere [closed]

The space between two concentric spherical shells of radii a, b (a < b) is filled with a liquid of density p. If the shells are set in motion, the inner one with velocity U in the x-direction and ...
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### Vertical Velocity Calculations

I've heard vertical velocity is at a maximum the instant a projectile is launched/thrown, it then decreases until the vertical velocity reaches 0, then lowers until it hits the ground. How do you ...
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### How would I go about solving a rigid body kinematics problem like this slider-crank exercise?

How might I go about solving this problem, would you mind walking me through it? I see that I need to build a system of equations around the acceleration of the two points in order to find the moment ...
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### Path of particles moving from the corners of an equilateral triangle toward each other at a constant rate

So I just was solving this standard problem when a question struck my mind. What is the nature of this path? I tried my best and all i was able to do was to prove that it is not a circle. Here is the ...
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### A problem concerning the rate of two ships

Two ships from one port to another, a distance of 825 nautical miles on the same direction, the speed of one ship being 4 knots faster than the other. The fast ship leaves the port 2 hours after the ...
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### Pursuit curve on a sphere

One day I thought about chasing curve on a sphere. I wanted to find parametric equations such as θ(t) and ϕ(t) of running dog always towards a rushing cat on a big spherical world. Orange point is ...
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### How can I get a new position using a turning angle, the previous point, and an amount of distance/delta time?

I'm trying to simulate kinematics and I have a previous point (x,y), an amount of distance the point will have traveled in this time step, the current heading of the point, and an angle this heading ...
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### Can anyone help with this question about finding the total distance traveled on a velocity time graph?

Question about a velocity time graph for a partical
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### Two cars travelling, find minimum distance given a ratio of speeds.

Here is a question from a Cambridge practice paper. Year 12 standard, math B. It involves finding the time when the cars are at a minimum distance from each other (part a). I have solved part a below. ...
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### A kinematics question refering to a delay time of vehicle with constant velocity before decelerating, what is minimum time?

A motorist is traveling at a constant speed $v_0$ and is approaching a traffic light. He wishes to stop the car at the light. However, his reaction time, that is, the time it takes him to put his foot ...
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### Kinematics problem - Need help solving an integral from a surprisingly difficult problem

I only need to know how to calculate time (t), I'll be able to do everything else after that by myself, and I've really tried, but I reach a hellish integral (that I've tried to calculate, but my ...
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### Motion of Points around a Triangle

I came across this problem in the book "Problems in General Physics by IE Irodov"- Three points are located at the vertices of an equilateral triangle whose side equals s. They all start ...
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### How to prove that a constant T satisfies the equation $T^2 - 50T - 2400 = 0$ in this question?

A car and a bus are travelling along a straight road towards traffic lights. The traffic lights change at time $t = 0$, where $t$ is in seconds. At this instant the car has a speed of $15 ms^{-1}$ . ...
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### Planar Kinematics: Circular orbit?

Assuming that the Earth's orbit around the Sun is circular, determine the mass of the Sun. It is also assumed that the mass of the sun is much greater than the mass of Earth. It is known the Earth ...
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### Change rotation axis in 3D forwards kinematics

I need help to solve a problem involving some math and geometry. Inside my courses, I have this diagram which represents the equation of several point in space, along a kind of pendulum: diagram The ...
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### Kinetic Fokker-Planck Equation vs Kramers Equation

Is there any difference between the Kinetic Fokker-Planck Equation and Kramers Equation ? I have seen them both used as a name for the Kolmogorov forward equation describing the time evolution for the ...
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### Solving for Machine Dimensions of Cable Robot

I am building an open source cable robot similar to this except constrained to two dimensions. I precisely know the lengths of all four cables, and from them I would like to derive the locations of ...
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### Rotation Matrix Equivalences?

Given the following rotation matrix: $$R_{BA} = \begin{bmatrix} 0.2362 & 0.9412 & 0.2414\\ 0.7558 & -0.3341 & 0.5631\\ 0.6107 & 0.0494 & -0.7903 \end{bmatrix}$$ Is it ...
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### Strictly increasing function that represents displacement of straight-line travel with non-constant speed

I am trying to model the displacement of a straight-line travel that has non-constant speed (e.g. 100 m sprint, straight-line horse racing, etc.). The model only needs to be plausible; it does not ...
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### Determining Acceleration to Intercept Accelerating Object

I'm trying to determine direction in which a missile should accelerate to hit a target in a 3D space simulation. The position and velocity of the missile, as well as the position, velocity, and ...
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### Puzzle involving three travellers trying to arrive at the same time

I have a puzzle stated as follows: There are three friends travelling to a party from the same location. The party is $320$ kilometres away, and they must arrive at the same time. They have two ...
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### How to find the angular speed of the cylinder spinning when a bullet strikes against it?

The problem is as follows: The figure from below shows a cylinder spinning. Find the angular speed of the cylinder so that the perforations made in a minimum time by the bullet carrying a linear ...
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### How to find the elapsed time between two collars when they are sliding over a thin wire?.

The problem is as follows: The figure from below shows two brass cylinders sliding through a wire as a guiding line to hit the ground. The cylinders are released from point $P$. Assuming that the ...
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### How to find elapsed time for two trains to cross each other when they travel in the same direction?

The problem is as follows: Two trains which have different lengths each are going to meet by traveling on different tracks with speeds $v_{1}$ and $v_{2}$ respectively. They take $20\,s$ to cross ...
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### Is it possible to know the distance covered by a train by only knowing some lengths covered a certain amount of time?

The problem is as follows: A mass trasit train is slowing down its motion before getting to destination. Sensors in the tracks as read in the control room indicate that the train took $20\,s$ and ...
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### How to find the length of a tunnel when a man is running from the halfpoint of a train?

The problem is as follows: A train is cruising with a constant speed of $10\frac{m}{s}$. In the exact moment when it enters a $60\,m$ tunnel a man standing in the midpoint of the train starts running ...
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### What will be the elapsed time for a person standing a railway can listen a beep?

The problem is as follows: A shinkansen which cruising with a constant rate across a railway in Tokyo emits a warning beep during $2\,s$. Find for how long (measured in seconds) a student standing ...
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### Additional IGCSE Kinematics problem, Cambridge Oct/Nov 2011 0606/13 [closed]

Hi I am having problems with this question below, still have no teacher to help due to corona: A particle moves in a straight line so that, t s after leaving a fixed point O, its velocity vms-1 is ...
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### Linear model for vehicle kinematics

I am designing an MPC controller for a vehicle, but due to the kinematics, the resulting MPC problem is nonlinear, which is not desirable in my problem. I wonder if double integrator model of the ...
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### Relationship between velocity vector and speed?

Hi all, I'm not too sure if this belongs in the Physics or Maths stack exchange but i feel like this is the most suitable place for it. Could someone explain why the sum of two velocity vectors (i and ...
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### Given the length of two vectors, find the angles that end on a point (2d)

This is a bit like a very simple inverse kinematics, but should be so simple that it can be done exactly. Er, well, I think it can! Problem definition: given armLength0, armLength1, and target (x,y), ...
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### Can we solve this without using calculus?

Point A moves uniformly with velocity $v$ so that the vector $v$ is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity $u< v$. At the initial ...
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### Help with Vehicle Position from Velocity Equation

I performance test cars with a draggy, it measures the change in position over time... sound familiar? anyway.. see below. I was able to enter my acceleration data in numbers and plot the equation ...
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### Graphing a path using quaternions as the coordinate space?

I'm trying to write an animation sequence for a video game engine that uses quaternions. I've never worked with quaternions before and even though I've spent hours trying to get my head around them, I'...
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### Find the angle that lets you make a bendy pipe

I have a pipe with $n$ segments of equal length. I move the farthest end nearer than the combined length to make the pipe bend. How do I find the angle between each segment with only the combined ...
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### Acceleration of a particle varies with distance as $-kx$. The particle is initially given a velocity $v_0$. Find time take to reach initial point

$\newcommand{\d}{\mathrm{d}}$I am having a problem here because acceleration varies with distance, and I am not able to relate it with time \begin{align} a &=-\frac{kx}{m} \\ v\frac{\d v}{\d x} &...
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### Acceleration and speed from timed events

Basically I have data from a list which shows how an automated scenery truck should move. The guys in the who have given it have basically given me an acceleration time and deceleration (or negative ...
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### Parametric curve end tip orientation

If I have a parametric curve equation, say for a trefoil ($3_1$) knot $x = 15(t^3-3t)$ $y = 15(-t^4+4t^2)$ $z= -15(0.2t^5-2t)$ Suppose I plot this only between t=(-2,0). Say the coordinate at the tip ...
The following is part of a derivation of the formula $v=v_0 + at$: $$dv=a\ dt$$ $$\int dv=a \int dt$$ $$v=at+C$$ Since, a C appears on the right side on integrating $dt$ why doesn't it appear on ...