New answers tagged kinematics
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Difference in answer using relative motion and that without (Newtonian Mechanics)
A better way, for me, to solve the question: consider the equation of the position of each body:
S1 = -V1t + a1t²/2
S2 = v2t - a2t²/2
Therefore, the distance that separates them will be given by the ...
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Accepted
Need help in understanding Tangential Acceleration
Derivatives speak to the instantaneous behavior at a point. It is possible to have a 1st derivative that is non-zero and a 2nd derivative that is 0 at a point. They're simply measuring two different ...
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How can I detect when a car makes a turn using velocity vectors and account for speed?
As per the clarification in the comments, you're following (or in fact simulating) the motion of the car according to some constant time slices of size $\Delta t$. I think that a rather simple ...
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How can I detect when a car makes a turn using velocity vectors and account for speed?
Check out the Frenet-Serret formulas (https://en.wikipedia.org/wiki/Frenet–Serret_formulas).
You have a parameterization of a curve (vs arc-length)
$$ {\bf r}(s) $$
and get the tangent unit vector:
$$ ...
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How can I detect when a car makes a turn using velocity vectors and account for speed?
If you decompose the velocity vector $\vec{v}$ into a speed $v$ and the direction of motion $\hat{e}$ with $$ \vec{v} = v \;\hat{e} \tag{1}$$
For example, at some instant i the position and velocity ...
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How can I detect when a car makes a turn using velocity vectors and account for speed?
The concept you are looking for is force. Force causes accelerations as in $F=ma$. Acceleration is the rate at which velocity vectors change.
A force in the direction the car is traveling (E.G. ...
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Question about the the velocity and acceleration in tensor notation
This answer is based on Pavel Grinfeld's Youtube lecture.
The trajectory is parameterized with respect to time as a given. That is, the contravariant bases are expressed as a function of time $Z^i \...
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Why is $v^2= u^2-2as$ if acceleration is negative?
This is best understood in terms of energy and work.
Work is the name for the type of energy supplied when a force acts on a body which moves in the direction of the force. In such a case the work ...
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How is the $v^2-u^2 = 2as$ modified as $v^2-u^2 = -2as$
I have faced this thing the days I began kinematics. This is how you shall address it:
In kinematics equations of motion, we use v² = u² + 2aS, which by itself cannot be modified to v²=u²–2aS. The 2md ...
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How is the $v^2-u^2 = 2as$ modified as $v^2-u^2 = -2as$
I think it depends on whether the object is moving up or moving down. if the object is moving up, then the acceleration of gravity will slow down its motion. at the same time, gravity will accelerate ...
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How to find 4-acceleration scalar product in terms of $ds$ spacetime interval?
Both the 4-velocity and 4-acceleration are defined as derivatives in terms of the proper time. Consider a massive particle moving through a geodesic $\mathbf{x}(\tau)$ in spacetime in its own ...
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Minimizing travel time of a car given some confusing constraints
I am new to physics, and came across the same problem.
If one assumes that the maximum speed of the car is 100 km/h (as I initially did) then the car must "coast" because it achieves ...
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Why doesn’t a cart accelerate when I push it with a constant force?
If the cart moves at constant speed when you apply a constant force to it, then the work you are performing is being used to overcome some sort of internal friction in the cart, very likely the ...
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
In general if $v$ denotes the velocity, the rate of change of speed is
\begin{align*}\frac{\text{d}|v|}{\text{d}t} &= \frac{\text{d}}{\text{d}t} \sqrt{ \left< v, v \right> } \\&= \frac{1}...
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Yes, this happens all the time. Fire a gun, or throw a ball, or do just about anything that involves making something move. And ignore things like air resistance, curvature of the earth and so on.
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Prelude - a (hopefully) fun but counterintuitive geometrical fact
A nice fact which may be a bit counterintuitive, is that if you have a square with diagonal length $\ell$ and this length varies in ...
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Hint: In the projectile motion (without drag) the acceleration $\vec{a}=\frac{d\vec{v}}{dt}$ is constant. However $\frac{d|\vec{v}|}{dt}$ is not constant, since it is negative when the projectile is ...
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Equilibrium partitioning between two domains with different mobility
Let me rephrase the system that you propose into a more concise setting. The density of random walkers (or the probability density of finding a walker in a given position $x$) follows a Fokker-Planck ...
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Accepted
Simplification of the Differential Cross Section in Peskin and Schroeder
This exact calculation is done explicitly in Schwartz Quantum Field Theory and the Standard Model in section 5.1.2.
The important thing is that $|\mathbf{p}_1| \neq |\mathbf{p}_A|$ unless the masses ...
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