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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29 views

Can accelaration of a falling mass be positive when upwards direction is positive? What am I missing?

As shown in the figure: (+) direction is upwards displacement is y time=t Let's say that $ y=30-5t^{2} $ , thus the second derivative will give acceleration as -10 which is (-) as expected. Now let'...
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Does tension vary across length of rod when there is no acceleration?

I know that Tension $T$ across elements of rod will vary in the case when the rod is moving with acceleration, and for each element tension acting will be equal to $ma$ (towards left) where $a$ is the ...
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How do you calculate rate of closure between 2 points when they don't intersect? (see diagram below)

What I'm interested in is the angle when a certain rate of closure is reached. Here we go. A is a vehicle traveling directly toward B at $V=75 m/s$. B and C are fixed stationary points on the same ...
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Block slides down frictionless wedge on frictionless surface. Find accelerations of the blocks

I am working on a physics problem where a small block of mass $m$ slides down a wedge-shaped block of mass $M$ with an angle $\alpha$ to the horizontal that rests on a frictionless horizontal surface. ...
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Apparent wavelength received by observer in doppler's effect

I have a few doubts about Doppler's effect. Does the apparent wavelength received by the observer depend upon whether the observer is moving or not? $λ_{apparent}=\ \frac{v_{sound}\pm v_{source}}{f}$....
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How to derive 3rd equation of motion $v^2=u^2+2as$ using $F=ma$?

How shall I derive, $v^2=u^2+2as$ using the equation $F=ma$?
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When to use relative velocity in centre of mass problems?

I am confused about when we should use relative velocity of an object placed on a movable platform like a wedge while solving center of mass related dynamics problems. For example, in the first ...
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Doppler effect formula when the medium is moving

We know the basic formula of apparent frequency in Doppler's effect. $f'=\frac{v_{sound}\pm v_{observer}}{v_{sound}\pm v_{source}}f$. What do we do when the medium itself is moving, say with a speed $...
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Two masses connected by two pulleys with one of the masses on an incline [closed]

What are the accelerations of the masses? For mass one, summing the force in both directions $$\sum F_x= m_1g\sin(\theta)-T=m_1a$$ $$\sum F_y=F_n-m_1g\cos(\theta)=0$$ So the acceleration is for mass ...
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Inclined planes and motion [closed]

A particle of mass $2\;kg$ is fired up a smooth slope of length $4 \;m$, with initial speed $10\;m/s$, inclined at an angle $30^\circ$ degrees above horizontal. What is the speed of the particle at ...
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Can anyone expound this Projectile Motion computation please?

I have this formula for projectile motion that I'm using in Unity game engine for getting the low or high Velocity of a projectile depending on how close or distant the target is (as long as it is ...
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One ball is dropped at a height, and another ball is thrown up with the final velocity of the first ball. Where do they meet? [closed]

I've found variations to this problem on stack exchange, but in most of them the initial velocity is varied. In this version, you first drop the ball at the top of the building, and measure its final ...
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Computing the tension force

There's this very simple problem which I've never quite been able to wrap my head around, partly because different instructors have given me different answers and, further, even looking at worked ...
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1answer
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Where am I going wrong in this derivation of second equation of kinematics?

I was trying to derive the $s=ut+\frac12at^2$ equation, where $s$=displacement; $u$=initial velocity; $t$=time taken; $a$=acceleration, on my own with some different ways; so I took $$v=\frac st$$ ...
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Acceleration of cylinder both rotating and moving under force from a pulley [closed]

The following states the problem 1.2 from the book Lagrangians And Hamiltonians by Patrick Hamill. A cylinder of mass $M$ and radius $R$ is set on end on a table at a distance $L$ from the edge, as ...
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On a rainy day, a man is running on a hilly terrain in such a way that he is always finding the rain drops hitting him vertically

It is assumed that rainfall is uniform in the whole terrain from O to E(figure attached) When the man was at rest on stretch OA, he found the rainfall at an angle of $30^o $ with the vertical. What ...
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1answer
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Force acts only along the length for a massless rod but not for a rod having mass? [closed]

In a question it is said that there are two balls A,B of mass m each attached to the ends of a massless rod and it rests on a smooth horizontal surface. Another ball of mass 2m moving with velocity u ...
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1answer
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Exact distance travelled by an object due to gravity only

I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
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In the kinematic equations $\vec{v}^2 = \vec{v}_0^2 + 2\vec{a}\cdot \Delta \vec{x}$, what does squaring a vector mean? [duplicate]

One of the kinematic equations, $\vec{v}^2 = \vec{v}_0^2 + 2\vec{a}\cdot \Delta \vec{x}$, involves squaring the initial and final velocities. My questions is, if velocity is a vector, what meaning ...
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Relative position from two reference frames

Here, clearly $\vec{r}_{S'S} + \vec{r}_{PS'}= \vec{r}_{PS}$. Then we differentiate and double differentiate and get the standard equations of relative velocity and acceleration. Now according to my ...
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Find a reference frame for a straight line rigid system

A body reference frame is a reference frame moving with a rigid body. So any rigid system has at least two points $P$ and $Q$ and these are such that $$ \vec{QP}\,\cdot\,\vec{QP}=\text{constant} $$ by ...
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What do we mean when we say constant or uniform?

What are the meanings of the terms constant and uniform in general? Constant: is it something that doesn't change or changes constantly? If yes, then what is uniform? Are they both same?
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Deriving smallest possible launching angle such target hits a point from geometrical envelope

I'm trying to understand fact-8 in page -9 of Jaan Kalda's PDF, Fact 8: If target is same level as cannon, then the optimal launching angle (corresponding to smallest launching speed is 45 deg) ...
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Determine droplet velocity from equation of motion

In multi-phase fluid mechanics the equation of motion for a drop can be described as follows: $$ \frac{\mathrm{d}v}{\mathrm{d}t}=\frac{f}{\tau_v}(u-v)+g $$ $g$ is acceleration due to gravity, $u$ is ...
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Given that $m \dot v \cdot v = 0$ , how is it equal to $m \frac{d}{dt} (v \cdot v)/2$? [closed]

While studying about scalar triple product in vector algebra, I stumbled upon the following question with the solution. I want know how is $m \dot v \cdot v $ = $m \frac{d}{dt} (v \cdot v)/2$?
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What causes displacement?

I'm doing this physics question, which I'll paraphrase: A car being driven at a constant speed 20 m/s in a straight line goes through a school zone. The car passes a tree, behind which a police car ...
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Visualisation tool for different speeds? [duplicate]

I'm a student often doing kinematics word problems with objects moving at X km/h, Y m/s, or Z cm/s. Yet, I have no idea what these units look like in real life. Out of curiosity, I'm searching for a ...
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Why do we say the resultant vector as the relative motion in this case?

If a car A moves with acceleration $2m/s^2 $due east and car B moves $1m/s^2 $due north. What would be the acceleration of car B with respect to car A. Now , for this. The solution in my textbook is ...
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Which is the centripetal term here?

In spherical coordinates the acceleration can be written as $$\textbf{a} = \dot{\textbf{v}} = \ddot{r} \hat{\textbf{r}} + \dot{r} ( \dot{θ} \boldsymbol{\hat{\theta}} + \sin θ \dot{\phi} \boldsymbol{\...
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Will there be a component of acceleration perpendicular to the surface along which a particle moves?

A particle is sliding in a cone maintaining contact with it all the time. Analyzing the situation in spherical coordinates I was able to find that in the total acceleration of the particle there will ...
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Finding the displacement of a drag racer

Sorry for asking such an obtuse question but I have no one to resort to about the following explanation for the answer below. I'm self-teaching myself physics so please don't be so hard on me and ...
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Bow and Arrow problem

Let say we have one big massive bow that could accelerate a smaller bow instead of an arrow but this smaller bow could accelerate a small arrow. If the big bow accelerates the smaller bow at $100$ Km/...
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Is it possible to find an explicit relation between these two, meaning that if one is given we can find another?

We know that the motion of a point on a space can be given as $\vec r = \vec r(t)$, where the vector is the position vector of the point or as $s = s(t)$ where $s$ is the coordinate of an arc on the ...
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Why is it advantageous to use to moving two particles to collide in a head-on collision, over a stationary target?

I have seen similar questions on this topic but I am more specifically wondering for particle accelerators what the effect on momentum and its relation, (if there is one) to the de Brogilei wavelength....
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How do I derive this formula? [closed]

How do I derive the range of a projectile formula? $$d = \frac{v\cos\theta}{g} \left( v\sin\theta + \sqrt{v^2 \sin^2\theta+ 2gy_0} \right)$$
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3answers
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How do they derive these formulas? [closed]

I've been doing some practice problems and they use formulas such as $$x=\frac{v_0^2\sin(2\theta)}{g}$$ $$\Delta y=\frac{v^2\sin^2(\theta)}{2g}$$ Can somebody please inform me on the ways in which ...
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Confusion Unit of Acceleration

I have been reading Newtonian mechanic but I got confuse in defining the unit of acceleration that "Why is the unit of acceleration $m/s^2$"?
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1answer
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Why do we need a Centripetal Acceleration formula?

Please excuse the stupidity in the question if there is any. Why can’t we use the average acceleration formula for centripetal acceleration? Why do we need to derive another formula for it. In its ...
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How can to get $v(t)$ out of this acceleration graph? [closed]

How can I get v(t) out of this acceleration graph?
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How to calculate number of turns and stops a car made from time speed and heading degree?

I have dataset that looks like this but more rows and need to have a function to return number of turns and stops during this trip.
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Which kinectic energy in an unreferenced system?

I wake up after an indeterminate period of hibernation. I'm in the dark deep space. No reference at all. I don't ear the hum of the engines. I can't know whether my starship moves inertially or it has ...
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1answer
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Gravitational field of a moving object

Here's a simple scenario: Let's say, that there are 2 stationary planetoids of equal mass on the Earth's orbital motion path, placed at equal distances from Earth just like on the image below: Will ...
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1answer
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Difference between transverse and tangential components of velocity

I couldn't understand the difference between two different formulations of velocity of a moving particle. In one formulation, we have radial and transverse components of velocity. In the other, we ...
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1answer
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How do you solve this Kinematic question? It's very non-standard [closed]

There are 4 beatles (John, Paul, George, and Ringo) on the vertices of a square with side length a, each beatle is moving in a constant speed v and in the direction of the beatle that started at the ...
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1answer
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Projectile Motion, get velocity and angle knowing distance and max height [closed]

I have been trying to figure out how to solve it. I know how to get the velocity by the distance and how to get the max height. Distance: $d = V_0^2 \cdot \sin(2\cdot\alpha)/g$ Max height: $h_{max} = ...
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Do conserved quantities tell us more general pattern than what we are taught?

Last year I had a question in m mind that as $mv$ (momentum) and $mv^2/2$ (Kinetic energy) both are conserved then n a closed system and they are dependent on same quantities and look very similar so ...
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2answers
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Rendezvous between two accelerating objects from opposite sides [closed]

I have two objects. Object 1 is travelling from A to B, a distance of (let's say) 1,000,000km. It can accelerate at 2g, and will accelerate up to the halfway point and then decelerate until the end (...
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1answer
71 views

What is the speed of a satellite?

Linear velocity $v$ is by definition the runned space $ds$ per time $dt$ elapsed: $v=ds/dt$. If the time elapsed in a specific point on the earth's surface is $t$, the dilated time elapsed on ...
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2answers
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How do we implement the speed differential for the Ackermann steering?

I'm working on a vehicle that uses four independent motors to control both the steering and speed for each wheel. I'm using Ackermann steering, and I've already got the steering angles down for the ...
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How do you calculate the minimum velocity for this problem? [closed]

I need help with the question below. I have started with that the distance travelled in the x - direction has to be greater than 2R and the same goes for in the y - direction. I then used the ...

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