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 cant the range of a projectile be calculated as the horizontal velocity multiplied by the time it takes the projectile to fall?

If I am given an angle, initial velocity, and initial height, I can calculate the time it takes for the projectile to hit the ground by using -(initialHeight) = Voy(t) - 5t^2. Now that I have the time ...
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$t=0$ is out of the domain of the equation of motion

At $t=0$, $Q_1$ is dropped under the influence of only the electrostatic force. I have solved the differential equation to find the equation of motion: and the distance of the 2 objects as a ...
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4answers
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Newton first law of motion

The State of rest and the state of uniform linear motion are equivalent. Why?
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Classic River swimmers problem [closed]

The problem states that Two persons at the bank of a river start swimming simultaneously at the same speed with respect to water. One person swims perpendicular to the stream in such a direction that ...
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1answer
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Hurricane - trajectory in a logarithmic spiral

Let $f : [0,\infty[ \longrightarrow [0,\infty[$ be a given function and consider a particle on the plane such that the particle starts at point $p_0$ at time $t=0$, its trajectory $t \mapsto p_t $ is ...
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Integrating product of Dirac deltas and step functions [closed]

I have the following integral $$\int d^4\boldsymbol{x}' \,\delta\big[(\boldsymbol{x}-\boldsymbol{x'})^2+\alpha^2\big]\,\Theta(-x_0+x'_0)\,\delta\big[(\boldsymbol{x'})^2+\alpha^2\big]\,\Theta(-x_0'),$$ ...
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3answers
549 views

Greatest distance between a particle moving with constant velocity and a particle moving with constant acceleration

Two particles start moving along the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity $u$ and the second with constant ...
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Slow down object to given speed in given distance [closed]

I have a problem. I have this data: my speed: 100km/h destination speed: 50km/h braking force: 8000N How to calculate distance needed to slow down my object? I dont want to look at other forces. ...
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How to use Whewell equation to find Velocity and acceleration? [closed]

Question How to use the following information to answer this question? $$\vec{v}(t)=\vec{r} '(t) ,\qquad \vec{a}(t)=\vec{r}''(t)$$ My attempt to answer this question.
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1answer
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Why intuitively is the tangent vector the derivative of velocity of position with respect to their modulus?

When trying to find the tangential velocity, many textbooks define the tangent direction as one of the following: or Intuitively, why is the tangent vector the derivative of the position with ...
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3answers
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Trivial uniform acceleration motion question [closed]

There is a question which to me (someone who knows very little physics) sounds a bit easy to solve, but I can't figure out what I did wrong here. QUESTION A person climbs 800 meters per hour. After ...
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1answer
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Speed of atoms being pushed away

It is said that it is impossible to calculate one-way speed of light. I have doubts in my small theory and I would like someone to correct me because I lack in knowledge in physics, and I'm surely ...
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Some introductory 1D falling motion problems to check the answers to [closed]

So I have the following problems for an introductory mechanics course (AP Physics C in high school, if anyone is familiar with it), and I got the following answers (using g = 10). Can someone check ...
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1answer
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If the earth spins at roughly 1,118.4 mi/h and you are speeding down the highway at 115 mi/h, what does a cop's radar read? [closed]

Hypothetically, if the earth spins at roughly 1,118.4 mi/h and you are speeding down the highway at 115 mi/h, what does a cop's radar read? Also, if the earth is spinning at 1,118.4 mi/h and you are ...
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Converting jerk function of distance to jerk function of time [closed]

When free falling inside a gravitational field, the jerk as a function of $r$ (the distance from the center of the Earth) is $$j(r)=\dot{a}(r)=-\frac{2GM}{r^{3}}.$$ Now suppose we have an apple that ...
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For the given motion of the object in the velocity-time graph, which of the following relations are true? [closed]

The velocity-time graph of a particle in one-dimensional motion is shown in figure. Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_{1}$ ...
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Kinematic question

I am trying to solve Problem 1.20 from Kleppner and Kolenkow book on Mechanics: Their solution is: which I understand. Notice that this results in $t_0 = 10.08s$ and $t_1 = T-t_0 = 12.50s $. However,...
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Displacement and distance for a particle travelling in straight line [closed]

A particle travels along a straight line with a velocity $v= (12 - 3t^2)$ m/s , where $t$ is in seconds. When $t$ = 1 s, the particle is located 10 m to the left of the origin. Calculate displacement ...
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How to translate force into upward hinging motion between two panels? [closed]

How to create a hinged joint between two panels where the hinging motion is actuated simply by pushing the panels together as they lie flat? Pictured below are two hinged panels that can rotate upward ...
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2answers
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How do we know if a particle is moving or not?

if there is only one particle in the universe, how do we know if it is moving or not? We don't have any other object to track the distance between the two, then is it possible to determine the ...
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What is the velocity of the bike? [closed]

On integrating $f(a)$ in the first phase where the $v$ is constant(since the acceleration is equal to $0\ \mathrm{m/s^2}$), I get $v_{t_1}$ is equal to $12\ \mathrm{m/s}$ and $v_{t_2}$ is equal to $0\ ...
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1answer
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Speed equation - why are the constants negative?

I want to show that the the equation $a = \dfrac{dv}{dt}$ leads to $v=v_0 + at$: $$a = \dfrac{dv}{dt}$$ $$a\, dt = dv$$ $$a\int dt = \int dv$$ Why do we chose a negative sign for the constants here? ...
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Straight Motion Kinematics Equation [closed]

Please explain to me, for the interval $15\leq t\leq 20$, why $x(t)=x(15)+8t=x(0)−160+8t$ with $v(t)=+8$, and the positive sign (+) indicates the direction to the right.
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1answer
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For competitive swimmers, why does drag increase when pushing off of the wall near the surface rather than deep in the water?

I found this experiment which showed that there is the least amount of drag between 1.25 and 1.50m below the surface of the water, while there is increased drag at just 0.25m below the surface. The ...
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Q: How to find the height of lake given time [closed]

I'm struggling with a Kinematics homework question: On a beautiful day you decide to go fishing with your younger brother Ben. Ben has not been fishing before so he doesn't know how to properly cast ...
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1answer
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What can I assume about Mandelstam variables in four-photon scattering?

In the case of four-photon scattering, the Mandelstam variables must satisfy $s+t+u=0$ Where: $ s=-(p_1+p_2)^2, t=-(p_1+p_3)^2, u=-(p_1+p_4)^2 $ And we know that $s>0$ is true because it is the ...
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2answers
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Force from time and velocity

Let's say I have a goal velocity $(v)$. In $n$ amount of time $(t)$ (let's say two seconds). What is the formula for finding the amount of force I would need (not counting other forces like drag/...
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7answers
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The direction of the velocity of a body can change when its acceleration is constant. How is it possible since acceleration is a vector quantity?

As we already know that acceleration is a vector quantity which means that it has both direction as well as magnitude. It can also change given any one of the two or both (magnitude and direction) ...
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Conservation or energy problem. What am I doing wrong? [closed]

For a given ion with a charge of $+1$ being accelerated by $U$ volts the distance it travels in a time $t$ is $d$ given by: $$d = v_0 t + \frac{1}{2} a t^2$$ for $v_0=0$ $$a = 2\frac{d}{t^2}$$ and for ...
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If my displacement is Euler's number $e$

So, differential of $e^x$ ($e$=Euler's No.) is equal to $e^x$. Now imagine I put $x=1$ and travel with a displacement $e$ (which is a constant) so we will be not moving anywhere since our displacement ...
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51 views

Acceleration and Reference Frames

If I'm in a car and hit the gas, an outside observer on the ground sees my car accelerate to some speed, and given the mass of my car and the horsepower of my engine, this obeys Newton's second law. ...
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1answer
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Stone falls from a balloon thats descending @ 12 m/s. What will be the displacement of the stone from the point of release after 10 seconds? [closed]

Question based on Motion in a Straight Line: “A stone falls from a balloon that is descending at a uniform rate of 12 m per second. What will be the displacement of the stone from the point of ...
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Equation of motion of a classic inverted pendulum in free fall

I was thinking in this interesting problem: Suppose we have this inverted pendulum: But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
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5answers
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Conflicting intuitions about free fall

So I just started studying physics recently, and I came up with a question that I'm not sure how to solve, and I think it may be because of some fundamental misunderstanding. I don't want anyone to ...
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Are quantum dot’s immobile?

In a recently closed question regarding the cooling of quantum dots through lasers has one of the commentators state that this is in fact impossible as QD’s are immobile: Can quantum dots temperature ...
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1answer
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Will the change in kinetic energy during projectile motion always zero?

Will the change in kinetic energy i.e. $\frac{1}{2}mv^2-\frac{1}{2}mu^2$ always zero in case of projectile motion since the initial speed and final speed is the same that is $u$? If my observation is ...
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1answer
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Calculating time for a biker to coast down a hill [closed]

A biker has traveled $79$ m up a hill inclined at $33.0^{\circ}$. At some point, the rider stops and coasts back down the hill. How much time does it take to make it back to the bottom of the hill? ...
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Why does a swimmer cross a swimming pool in the same time as crossing a flowing river?

I read that the time taken to cross a swimming pool (still waters) is the same minimum time required to cross a flowing river, provided the swimmer crosses it the river in the minimum time required, ...
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3answers
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How is position calculated when the acceleration is not constant?

To get the position of an object we can use the equation: $$x=x_0+v_0t+\frac{1}{2}at^2$$ But now I don't have a constant acceleration, both $x_0$ and $v_0$ start at $0$ and $v$ ends at $16 \text{ m/s}$...
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2answers
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A doubt regarding this statement about motion in polar coordinate system

There was this statement in my book that was not quite clear to me even after reading it after 20 times, the statement was: There is a fundamental difference between polar and Cartesian base vectors: ...
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2answers
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Space debris impact

Given two pieces of aluminum, a sphere with diameter $d$ and a plate, how can we estimate the penetration depth given the initial velocity $v$ of the sphere? If that proves too complicated due to ...
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2answers
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Distance and velocity increased by $g$ units every second

Distance fallen in every second gets increased by $g$ units. Velocity is increased by $g$ units every second. Is it true that distance and velocity increases by $g$ after every second? If it starts ...
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Statistical Analysis of motion under central force

My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
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3answers
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Is centripetal acceleration almost perpendicular to velocity or it is exactly perpendicular to velocity?

In all the derivations of centripetal acceleration that I have seen so far, the direction of acceleration is said to be perpendicular to velocity but I think it's not exactly perpendicular to velocity ...
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1answer
70 views

Why temperature of an object doesn't change when that object is in motion? [duplicate]

Temperature: Measure of random kinetic energy of molecules Here's what I'm trying to say we have two book, and we place on book on moving truck and other on ground, so according to definition our ...
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1answer
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Deriving law of velocity in simple harmonic motion

The traditional way of deriving velocity equation in SHM is: But I wanted to derive it using pre-calculus and some basics. I couldn't pass this step:
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Some help in understanding energy conservation relating to special relativity

Consider the decay of particle $A$ into particles $B$ and $T$ where $T$ is the tachyon particle. The conservation of energy equation can thus be expressed as $$m_A=\sqrt{p^2+m^2_B}-\sqrt{p^2-m^2_T}\,.$...
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1answer
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How to calculate the speeds two objects need to move at in order to reach different destinations at the same time [closed]

For example: On a graph there are two points. Each point has a different destination. The distance between Point A and its destination is 50, and the distance between Point B is 100. The points will ...
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1answer
35 views

Minimum launching speed projectile constraint

I came across an interesting lemma in page-9 of Jaan Kalda's Kinematics handouts, the following is written: When a target is shot with the smallest possible launching speed, the trajectory and the ...

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