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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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The product rule and the third kinematic equation

I'm trying to find physics-based examples for the rules of calculus. Using the product rule on the third kinematic equation to find the velocity is one such example. I'm deriving the correct equation ...
mmm111mmm's user avatar
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1 vote
1 answer
40 views

Confusion about inverse kinematics of simple double-jointed arm

I hope this doesn't come across as too much of a check-my-work. If not, please let me know of a better site for this, or I'd appreciate being moved. I'll get straight to the point. I'm trying to ...
HydroPage's user avatar
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0 answers
11 views

How to use BCH formula to compute mutiplication of group element?

i cant get the right answer. Given the commute rule of (for example, the caculation below will be in static group): we have: generator H, P, K, J, and commutation rule $[H,P]=0$, $[H,K]=0$, $[P,P]=0$...
showin's user avatar
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2 votes
3 answers
108 views

Time to reach max height with an inverse square law relationship for gravity.

A spaceship is launched from Earth's surface with acceleration given by $$ a = -\frac{gR^{2}}{x^{2}} $$ where $g$ is the acceleration due to gravity at the Earth's ...
weekly5112's user avatar
2 votes
2 answers
42 views

Covariant and contravariant velocity

I'm facing the following problem in tensor calculus: I want to calculate the velocity of a mass particle in spherical coordinates. So I'm using the following coordinate functions for spherical ...
user avatar
0 votes
0 answers
20 views

Rotating -axis relative motion, the acceleration of the origin of the rotating frame

I have a question of 3D kinematics of a rigid body. For relative motion analysis, let's define XYZ as an inertial frame, and xyz with origin O as a rotating frame. If we want to find the time ...
Sujin Bureerat's user avatar
0 votes
1 answer
57 views

Target position given ship velocity and bullet velocity.

Let's say we have two ships. Both have a velocity and the first ship has a turret with autotargeting. For simplicity let's say the ship is a point and a bullet comes out of that point. The first ship ...
Vinny's user avatar
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0 answers
33 views

Free-Surface kinematic BC - Azimuthal suspended flow - cylindrical coordinates - How to define the free surface and derive its impermeability?

I am working on a linear stability analysis of an azimuthal free surface flow. However, I am stuck in the derivation of the kinematic BC to apply for the impermeability of the azimuthal free surface (...
Virgil 11's user avatar
1 vote
0 answers
31 views

I have two formulations of quadrotor dynamics, one in euler angle velocities, and one in body frame angular velocities. I am unable to see equivalence

In the following MIT lecture notes Equation (6.10) is on the following form \begin{equation}\begin{bmatrix} m \dot{v}^w \\ J \dot{\omega}^B \end{bmatrix} = \begin{bmatrix} -mge_3 \\ -\omega^B \times J ...
joh's user avatar
  • 11
3 votes
1 answer
206 views

Why acceleration is not always parallel to velocity but velocity is always parallel to displacement?

Velocity is derivative of displacement : $$\vec v=\frac{\mathrm {d\vec r}}{\mathrm dt}$$ And acceleration is derivative of velocity. $$\vec a=\frac{\mathrm {d\vec v}}{\mathrm dt}$$ Given that their ...
An_Elephant's user avatar
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1 vote
1 answer
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Circles,projectile motion and parabola

Q) A projectile is thrown at an angle theta from O(0,0) and reaches R(R,0) given R is the range of projectile A point P is taken on its trajectory and is joined with O(0,0) and R(R,0) such that angle ...
Sankalp Kumar Jha's user avatar
1 vote
1 answer
58 views

Deriving the Maximum Range of a Particle With A Constant Force Using Geometric Algebra

I am learning Geometric Algebra by reading New Foundations for Classical Mechanics, by David Hestenes. Chapter 3-2 studies the motion of a particle with constant gravitational force and on page 129 ...
Cereza's user avatar
  • 11
0 votes
0 answers
42 views

Maximizing Speed on an Elliptical Path

I'm currently delving into a problem that involves analyzing the motion of a particle moving along an elliptical path in the plane, and I could really use some help figuring out a couple of aspects. ...
tarek hankir's user avatar
1 vote
1 answer
54 views

Need Help with Particle Motion Analysis in $\mathbb{R}^2$

I'm currently working on a problem related to particle motion in the plane $( \mathbf{R}^2 )$ and could use some guidance. The particle moves along a curve, and at any given time $( t )$ seconds after ...
tarek hankir's user avatar
1 vote
1 answer
94 views

Time taken for a bead to slide down a wire.

A circular hoop of radius $r$ is stood vertically on a flat surface and held in place. A smooth wire is tightly stretched between the upmost point of the hoop and a point on the hoop at height $h$. A ...
Developer's user avatar
0 votes
1 answer
45 views

Calculating acceleration from velocity as a function of distance [closed]

This comes from USA Harvard-MIT Mathematics Tournament (I don't know from which year) A particle moves along the $x$-axis such that its velocity at the $x$-position is given by the formula $v(x) = 2 +...
Gennaro's user avatar
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1 vote
1 answer
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Is there a way to represent the 4th kinematic equation of velocity squared visually?

Kinematic Equations: \begin{align} v &= v_0+at \\ \Delta x &= \left( \frac {v+v_0} 2 \right) t \\ \Delta x &= v_0t + \frac12 at^2 \\ v^2 &= v_0^2 + 2a\Delta x \end{align} So for the ...
jack's user avatar
  • 21
1 vote
1 answer
108 views

Calculating the time taken for a bouncing ball to come to rest.

A ball is dropped from rest at a height $h_0$ and bounces from a surface such that the height of the $n$th bounce, $h_n$ is given by $h_n=αh_{n-1}$, where $h_{n-1}$ is the height of the previous, $(n-...
Developer's user avatar
0 votes
0 answers
39 views

How do I get a parabolic trajectory (in terms of Fy) of a bullet shot parallel to the ground if x(t) varies as t^0.5? (not as easy as one would think)

Let's consider a shallow-water free-surface jet exhausting in the X direction from a thin rectangular slot into a quiescent fluid. Within the jet the mean velocity field can be expressed as follows: $$...
Matteo Sollevanti's user avatar
0 votes
1 answer
113 views

Calculating the time of collision of two vehicles.

I have the following problem but I'm not sure how to get started. I have a car that is $14m$ behind a lorry. The car's initial velocity is $20 ms^{-1}$ and it is decelerating at $7.6 ms^{-2}$, whilst ...
Developer's user avatar
0 votes
1 answer
52 views

Please tell me how can we plot graph of position vector vs time curve

If you have a position vector $${\bf r} = x\hat{\bf i} + y\hat{\bf j} + z\hat{\bf k}$$ With respect to origin and independently each $x,y$ and $z$ coordinates are function of time then how can we ...
Suryansh Sharma's user avatar
1 vote
0 answers
87 views

Mutual perpendicular line between two axes

I'm going through a robotics textbook Introduction to Robotics Mechanics and Control 3rd edition by John J. Craig and am currently on a section describing the relationships between links of some ...
MAP3's user avatar
  • 21
0 votes
1 answer
100 views

Decay estimates for transport equations in massless case

Considering the kinetic-transport equation $f(t,x,p)$ in the mass shell. It is well known that in the classic case (Vlasov non-relativistic) \begin{align*} \int_{\mathbb{R}^3} f(t,x,v)dv &= \...
Gaiüx's user avatar
  • 3
1 vote
1 answer
75 views

What is this weird way to approximate the area under the curve?

This graph appeared in an exam question They calculated the area by using $\frac{1}{2} \times (6+3.8) \times 8$. I'm really confused because I only know how to find the area under the curve using 3 ...
John Hon's user avatar
  • 473
1 vote
0 answers
83 views

Intuitive reasoning why the integral of dv is velocity?

I'm struggling to understand the geometrical/physical meaning behind why $\int_{v_0}^{v_f} dv=v$, especially how this relates to the area under the curve. I was recently looking at the following ...
Mosrod's user avatar
  • 11
0 votes
0 answers
33 views

Rearranging trigonometric equation for low speed vehicle turning geometry

I have a set of equations that describe the geometry of a vehicle in low speed turning (a single track vehicle with the assumption that the tyres go in the direction they are pointing). A constraint ...
Simon Aldworth's user avatar
0 votes
1 answer
91 views

Will a particle initially at rest at origin with acceleration as square of its x-coordinate ever move?

Cross posted from Physics Stack Exchange because this seems to mostly be a mathematical problem. Consider a particle such that at $t=0$ (time), $x=0$ (x-coordinate) and $v=0$ (speed). Let $a(x)=x^2$ (...
brainfreeze's user avatar
0 votes
2 answers
95 views

A tricky question on kinematics asked in a competitive exam

So I found this rather ambiguous question based on kinematics from a competitive examination, the question with options is - A car travels in such a way that its velocity becomes twice the previous ...
Nirmish Sarmalkar's user avatar
0 votes
0 answers
41 views

IMU frame to body frame

I am just wondering how do we transfer IMU readings to Body frame? Especially, linear speed and acceleration. In following diagram, the IMU is mounted on one of the surfaces of the body (you can ...
Nick X Tsui's user avatar
0 votes
0 answers
27 views

How to integrate arbitrary discrete-time linear and angular body fixed velocity to world space?

I have body fixed angular velocity values and linear acceleration values streaming in to my application. at some interval $\delta t$. I need to get a world position from these, assuming the start ...
craigB's user avatar
  • 133
1 vote
1 answer
133 views

Integrating $\int \frac{d\theta}{\sqrt{a-b \sin \theta}}$ [closed]

I was looking into rotational motion in physics and encountered this integral where a and b are constants. $$\int\frac{d\theta}{\sqrt{a-b \sin \theta}}$$ I have found that it looks like an elliptic ...
user1244595's user avatar
1 vote
1 answer
54 views

Do all planar rigid graphs contain a triangle?

If one looks at rigid rod and joint linkages (such as the Laman graphs) one instantly notices a similarity between them, which is that all of them either contain $K_3$ or something which contains $K_{...
Jonathan Beer's user avatar
1 vote
1 answer
46 views

Find plane of symmetry (knowing reflection positions)

I have a set of 3 distincts points which I know the positions in 3D (say D1, D2, D3). I also know they are the plane-symmetry of 3 other distinct points in 3D (say B1, B2, B3) which I also know the ...
CitizenInsane's user avatar
-1 votes
1 answer
136 views

Solve Max Velocity given Distance, Time, Initial velocity and final velocity [closed]

Following is known: vInitial = 0 mm/s, vFinal = 100 mm/s, totalTime = 0.9 sec, TotalDistance = 100 mm How can I calculate the maximum velocity that will be reached, considering constant acceleration ...
Arsalan's user avatar
  • 11
0 votes
1 answer
30 views

finding the greatest distance reached above the ground [closed]

question mark scheme answer I don't understand why there is an additional $0.441$ added to the final distance... I do understand that the distance travelled by $A$ downwards is equal to the distance ...
wjkrkdfjkn's user avatar
-2 votes
1 answer
49 views

Simple Kinematics (v-t graph) [closed]

A particle moves in a straight line. Its velocity–time graph is shown. a. After 165 seconds the particle returns to the starting point. Find the value of T. b. At what time does the particle have ...
Phazis's user avatar
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0 votes
1 answer
141 views

Which way does a stone move when hit by a wheel/tire? [closed]

I apologize if this question has been asked before, but I haven't been able to find a post which covers this exact question. Let's say that we have a driving car which is moving forward. At some point,...
Stallmp's user avatar
  • 346
0 votes
1 answer
117 views

Minimization problem of parametric equations in ballistics (minimum projectile speed)

I am trying to solve a minimization problem for a physics simulation in Unity 3D. In short, a projectile is fired at a certain position with a certain velocity, and experiences a constant acceleration ...
The Innkeeper's user avatar
0 votes
0 answers
31 views

Vector Method for a Related Rates Question

A standard related related rates question is: A ladder propped aganist a wall is being moved closer. If the distance between the wall and the ladder reduces by reduces by $a$ m/s, find the rate of ...
Starlight's user avatar
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0 votes
0 answers
92 views

Solution works for 2nd degree polynomial but does not extend to higher degrees.

(I am reposting this from physics stack exchange since they seem to not accept this type of question, and in my case it is also probably more math-focused.) I am trying to solve a 3D ballistics ...
The Innkeeper's user avatar
0 votes
0 answers
45 views

Manipulating multiplicity of polynomial roots based on coefficients

For context, I am trying to solve a ballistics problem in 3D where I want to find the minimum launch velocity of a projectile to be able to hit a moving target. The details can be found here. I ...
The Innkeeper's user avatar
0 votes
1 answer
64 views

How does autocorrelated noise models converge to white noise models when considering kinematic tracking models?

In the article: A jerk model for tracking highly maneuvering targets see http://eprints.iisc.ac.in/2710/ The jerk model is explained. What happens with the process noise matrix Q if the limit is taken ...
Eduard's user avatar
  • 63
1 vote
1 answer
125 views

Calculating projectile path between 2 moving objects for given force

For 2 moving objects A and B (mass $m_a$, $m_b$) moving with constant acceleration, given initial accelerations, velocities and positions for both objects, find the velocity required to launch a ...
The Innkeeper's user avatar
2 votes
1 answer
94 views

Combining rotations about different coordinate systems

I'm working on what I imagine is a common problem, but am struggling to find high quality resources. It is easiest to describe with an example: Let's say I have a series of frames and coordinate ...
Andrew Lock's user avatar
1 vote
1 answer
119 views

Find the parabola tangent to a point, such that the symetric tangent passes through an arbitrary point

I have a body $\vec{b}$ in a frictionless, gravityless plane, with an initial velocity $\vec{v}_i$. I want to redirect this body so that it's final velocity $\vec{v}_f$ has the same magnitude as $\vec{...
Croustitrain's user avatar
2 votes
1 answer
278 views

Solving a kinematics problem involving areas under curve

The Original question is as follows: Two cars $A$ and $B$ simultaneously start a race. Velocity $v$ of the car $A$ varies with time $t$ according to graph shown. It acquires a velocity of $50 m/s$ ...
An_Elephant's user avatar
  • 2,821
4 votes
3 answers
158 views

Launch angle of projectile motion not in terms of time

I have these two projectile-motion equations: $$ vt\cos(\theta)=d $$ $$0=h+vt\sin(\theta)+\frac12at^2 $$ Is it possible to derive an expression for $\theta$ in terms of at most $d, v, h, a$ but not $t?...
tophatcollection's user avatar
2 votes
1 answer
57 views

Highest point of a ball above a hill

A ball is thrown from the top of a hill at $32$ m/s, $60$ degrees above the horizontal. The hill slopes downwards at a constant angle of $30$ degrees below the horizontal. The acceleration vector is ...
stefan's user avatar
  • 21
-1 votes
1 answer
326 views

Integrating the velocity vector

If we integrate the velocity vector with respect to time, do we get the displacement vector or the position vector? What I mean is that, do we integrate the velocity vector to get the displacement ...
Nav Bhatthal's user avatar
  • 1,057
2 votes
0 answers
44 views

kinematics - acceleration in terms of distance

A particle moves in a straight line and is at a distance $x$ from a fixed point $O$ on the line at time $t$. If $$12x = 27 + 6t^2 - t^4$$ find the velocity and acceleration of the particle at time $t$....
InquisitiveLad's user avatar

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