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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Why do kinematic equations only work with constant acceleration?

People say that the equations are derived assuming a constant acceleration. I just don't see how this is the case. (I am new to calculus.)
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Why do equation of motion fail to apply in non-inertial frame even after applying pseudo force?

I considered two cars of equal mass moving towards each other with speed 30m/s and 18 m/s respectively and when they are 100 meters apart they both start de accelerating at 6m/s² each. So if we ...
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Minimum seperation of moving objects doubt

Let there be $2$ objects $P_1$(initial velocity $u$ $ms^{-1}$ & acceleration $a$ $ms^{-2}$) & $P_2$ (initial velocity $U$ $ms^{-1}$ & acceleration $A$ $ms^{-2}$) initially separated by ...
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Can the speed of the wind influence the speed of sound propagated in it?

The question came up with a exercise (Page 5, exercise (vi) of Pratice Exercise 1.1) from the book Physics Galaxy Volume 1 Ed. 1, Ashish Arora. The question proposes the following: Two junglemen are ...
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Why power of engine must be equal to power of friction?

Suppose a car with electrical engine moves uniformly with friction between wheels and the ground (neglect air resistance, energy loss, etc.). So why the car's engine power must be equal to friction's ...
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Strange kinematics result

I'm currently doing some algebra-based physics problem sets and have come across this strange result. Problem A ball is tossed upwards with an initial velocity $\vec{v}_0 = 48.9\text{ m/s}$. Assuming ...
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Lagrangian Dynamics of an inverted Spherical Cart Pendulum

Introduction I have to come up with a PD-controller for an inverted Spherical Cart Pendulum, therefore I tried to compute the Dynamics of such a Pendulum. The Spherical Cart Pendulum is a hybrid ...
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A question regarding equations of motion

Suppose I drop a body from a height $h$. The initial velocity is zero. Now it reaches the ground and stops and finally becomes zero. So now u=0 and v=0. If I use the equation of motion $v=u+at$ to ...
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How can I find the amount of time required for this to stop? [closed]

A particle starts from rest and moves with a constant acceleration of 5 m/s2. It goes on for 10 s. Then, it slows down with constant acceleration for 500 m until it stops. How much time does it take ...
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How to find time taken for a faster object to cross a slower object of same length, both moving parallel to each other in the same direction? [closed]

Can you explain me how to determine the time taken for a faster object to cross a slower object when they're both of same length and are moving parallel to each other in the same direction?
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Is the deceleration a result of friction, a constant value?

Frictional Force = km, therefore k = a Would this mean that no matter the mass of an object (if they are the same material) They will decelerate at the same speed with friction, therefore if u is the ...
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Angle-free two-dimensional inelastic collision formula?

I'm trying to calculate velocities (by components - x, y) of two objects (balls) after inelastic, two-dimensional collision. I've successfully implemented the angle-free formula for elastic two-...
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Are bicycles the fastest possible human-powered vehicles? [closed]

It seems to me that bicycles have proven themselves to be the fastest human-powered vehicle in common usage. By “human-powered” I mean it has no fuel or power source other than the inputs given by a ...
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Deriving Formulas for a running person and a moving bus [closed]

A bus is going along a straight line with velocity v1. You are located at a distance D from the bus and distance S away from the road. You can run with a maximum speed v2 in any direction. a) In ...
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They accelerated covariantly [closed]

Show that if the 3 acceleration vector of a relativistic point mass is zero for a relativistic inertial observer then it is also zero for all relativistic inertial observers. This implies that ...
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Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction [closed]

I think I missed something in this mechanics problem. We're given a polished (no friction) and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it. There is ...
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Does the kinetic energy theorem imply that any body on wich is exerted the same space-dependent force is equally accelerated?

So, we have a body $P_1$ of mass $m$ that travels from $A$ to $B$ along a straight line, on wich is exerted a constant force $F$ dependent only on the position of $P_1$. We know that the work done is $...
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How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

Is there a way to correctly predict the direction of the unit radial vector and the unit transverse vector in problems like the one below or is it just better to take a guess and solve the problem ...
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Projectile with air resistance analysis

If a projectile is thrown neglecting air resistance, then the horizontal distance covered by it in ascent and descent is same. if we consider air resistance, then i want to compare horizontal distance ...
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Does tangential velocity not change the "radial displacement"?

For example, we have two point masses U and V moving like the picture below with constant velocity. Is the change on "relative position" in this case only affected by the velocity $u$ and ...
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Minimum energy of projectile to trigger a nuclear reaction and energy of ejectiles

I am studying the following type of nuclear reactions : projectile+target -> ejectile1+ejectile2 I make the assumption that the target is static. This reaction needs energy to be triggered (Q-value&...
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Closing speed and time needed for light to reach moving object

I've come across this kind of problems where I need to find a time interval for light rays to reach a moving observer. Suppose Bob is travelling towards a mirror at a speed $v$ relative to the mirror. ...
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Finding How to Transform a Plane to Reflect a Trajectory through a Given Coordinate

So, for context, I am trying to analyze how this basketball machine works: https://www.youtube.com/watch?v=FycDx69px8U I have a basic understanding of how to calculate the new velocity of the ball ...
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Simple harmonic motion in uniform circular motion as a projection along $x$-axis

The image shows the position of particle at $t=0$ and $t=t$, and the relevant angles are labelled. The radius of the circle is A. When I try to find $x(t)$ I can directly resolve along the negative $x$...
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Trajectory with non-trivial barrel length taken into account

I have pretty much the same question as this: Finding the Angle of Launch for a Cannon Projectile to Hit a Specific Point It wasn't answered back then, and I only found it after I made my own initial ...
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How to simplify three body decay phase space in terms of invariant mass $q^2$?

We know three body phase space is written as: $$\mathrm d\pi^3 = \frac1{2M_1}\frac{1}{(2\pi)^5}\int\frac{d^3 p_2}{2E_2} \int\frac{d^3 p_3}{2E_3} \int \frac{d^3 p_4}{2E_4} \delta^4(p_1-p_2-p_3-p_4)$$ ...
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1 answer
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Calculating the rest mass after relativistic collision [closed]

Suppose we got two particles, both of mass $m$ for simplicity, travelling at high speeds towards each other, meaning we have to take into consideration of relativistic effects. We also know that the ...
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Angular velocity of a particle in uniform circular motion about a general point

This problem was given by our professor. Consider a particle P executing uniform circular motion wrt the point O with uniform angular velocity $\omega$ anticlockwise whose cordinate is $(2R,0)$ in a ...
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Simple 1D Motion Problem

I am having a friendly debate with someone regarding the solution to a 1D motion test problem we both came across. It goes something like this (numbers changed to preserve integrity of test material). ...
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Vehicular Dynamics [closed]

Consider an open differential connected to two wheels on each side. The wheels are flat discs and are 1400 mm apart. This car is making a turn of radius 7 m at a constant angular velocity of 30 ...
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Can a particle move in an upward parabola fashion naturally?

I recently studied projectile motion which consists of only downward parabolas. But I was wondering whether is it possible for a particle to go in a upward parabola provided that the particle doesn't ...
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Calculate Projectile impact with a moving Target [closed]

I'm trying to solve the classic shoot moving object issue in 3D Space, but with acceleration and gravity added to it. I already tried several ways approaching the correct calculation, yet I face the ...
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How is the angle of the front wheel found in Bicycle Kinematics Model for a Car

My question is, in a 4 wheel model, the front wheels have different angles. To simplify things bicycle model is used. In the bicycle model, there is an imaginary wheel in the middle of the front ...
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Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?

Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral? Intro After seeing this videos about the ...
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What do you call $ \frac{d^2 r}{dt^2}$ in polar coordinates? [duplicate]

In polar coordinates, one finds centripetal acceleration as: $$ a_c = \frac{d^2 r}{dt^2}- \frac{v^2}{r}$$ Where $|r|$ is distance from center to particle, $v$ is tangential velocity. My question is ...
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Calculate efficiency from discrete power, time and distance

I have a sequence of points from GPS and OBD for some vehicles. Each point has the instantaneous power of the engine $(P)$, the time elapsed from the last points $(T)$ and the distance traveled from ...
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3 votes
3 answers
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Existence of uniform circular motion [duplicate]

We know that if any body has some mass and is moving with a velocity v at an instant $t = 0$ , then it is not going to have same velocity after some time if any net force acts on it. It is because the ...
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How to interpret a displacement-position graph?

I have a good understanding of Displacement-time graphs and position-time graphs and how to interpret them. I take the IB diploma and came across this question from a 2009 paper with a displacement-...
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Related bubble questions: In water vs air, what causes bubbles to form?

One thing I would guess would happen is that air released under water would diffuse through it as individual molecules rather than collecting as bubbles. I suspect the bubble effect might come from ...
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3 votes
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)

I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
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Running of the fine structure constant

In Measurement of the Running of the Fine-Structure Constant, the L3 collaboration reports their fine structure constant data for various values of momentum transfer which they call $Q^2$. This is ...
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3 answers
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Why does solving the differential equation for circular motion lead to an illogical result?

In uniform circular motion, acceleration is expressed by the equation $$a = \frac{v^2}{r}. $$ But this is a differential equation and solving it gets the result $$v = -\frac{r}{c+t}.$$ This doesn’t ...
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Is it possible for a point-like system to behave like $x(t) = \frac{t}{2}\log(t^2)$ near $t=0$? (infinite speed) [closed]

Is it possible for a point-like system to behave like $x(t) = \frac{t}{2}\log(t^2)$ near $t=0$? (infinite speed) I know beforehand that relativity theory forbids anything with mass from travel faster ...
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When should smartphone be declared as static using accelerometer reading? [closed]

I wish to know when should I declare an smart phone static by reading its 3 axis accelerometer reading. I have notice that modulo of all 3 axes gives 9.8 when ever smart phone is static. What does it ...
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Why is there a difference between single and double compound pendulum's kinetic energy equation?

When calculating equation of motion of single compound pendulum, kinetic energy is taken as $K= I\dot{\theta}^2/2$ (See). But when it is double compound pendulum, kinetic energy of the first pendulum ...
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13 votes
1 answer
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How can one detect a device (phone) falling using its 3-axis accelerometer?

I am working on an Android app to use its 3-axis inbuilt accelerometer to find if the phone falls. I googled and found that if the following value is less than 2: $$a = \sqrt{x^2 + y^2 + z^2}$$ (where ...
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3 votes
3 answers
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How do you find the final velocity when acceleration is changing between two values over some distance? [duplicate]

How do you calculate a final velocity of an object when given its initial velocity and the object is accelerating between an initial and final acceleration over some given distance?
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2 votes
1 answer
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The rate of change of speed when turning back along a straight line

I was trying to find how the rate of change of spped at $t$ of an object moving in a straight line relates to its maginitude of it acceleration. The case when it is moving in the direction before and ...
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1 vote
1 answer
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Constant velocity and linear acceleration

Given an object moving in a straight line with velocity that can be modeled by a parabola, would the answer to the question "when is the velocity constant" be the vertex of the velocity ...
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How is there kinetic energy at the bottom of the pendulum swing if velocity = 0 at the lowest point?

Say a mass $m$ is attached to a massless string that is attached to the ceiling. The mass is pulled 30 degrees to the left of the vertical and then let go. At the lowest point of its swing it has ...
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