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The value of $g$ in free fall motion on earth

$$F=-G\frac{Mm}{r^2}$$ $$\frac{F}{m}=-G\frac{M}{r^2}$$ $$a=-G\frac{M}{r^2}$$ Force divided by mass is by definition acceleration. This is denoted as g, as in, the acceleration due to gravity For the ...
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The value of $g$ in free fall motion on earth

You can see that $g$ has units of acceleration, namely $\frac {m}{s^2}$ or $\frac {m}{s} \left (\frac 1s \right )$. Last form gives an easy interpretation,- speed change per 1 second. Additionally, ...
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The value of $g$ in free fall motion on earth

The other guys here (@Thomas Fritsch and @AWanderingMind) are perfectly right, and just to see that: g is an acceleration, and acceleration is change of velocity with time, or velocity per time. Like ...
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The value of $g$ in free fall motion on earth

It means the speed increases by $9.8$ m/s every second. At the beginning (when you release the body) its speed is $0$. After $1$ second the speed is $9.8$ m/s, after $2$ seconds the speed is $19.6$ m/...
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2 votes

The value of $g$ in free fall motion on earth

It means the speed of the falling body increases with 9.8 m/s each second.
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1 vote

Confusion in coordinate transformation of acceleration vector

The confusion arises because one of the reference frames is moving w.r.t the other one. In your second eq. you are transforming one vector at the seme time, so it is just a coordinate transformation. ...
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How does negative velocity and positive acceleration exactly and vice versa slow down objects?

Consider a numerical example. At time $t=0\,s$ the constant acceleration of a body is $+2\,\rm m\,s^{-2}$ due East whilst it is travelling at a velocity of $6\, \rm m \,s^{-1}$ due West. So at time $t=...
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How does negative velocity and positive acceleration exactly and vice versa slow down objects?

You seem to be confusing velocity, which is a vector, and its norm. Newton's first law is about constant vector velocity: constant norm: the object moves with constant speed constant direction: the ...
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What exactly is happening to acceleration when direction changes?

very good question. we know that speed is a vector. for changing a vector, it needs to be added to another vector. this question, is a very good example to talk about steady state and transient state. ...
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What exactly is happening to acceleration when direction changes?

Direction of motion changes due to acceleration but there is not any compulsion that there should or should not be any change in acceleration when direction changes. For example when we throw a object ...
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1 vote

The utility of HorsePower vs Torque

Neglecting air resistance and other forms of drag the general expression for acceleration as a function of engine power (regardless of gearing etc) is $$ a = \frac{P}{m\, v} \tag{1}$$ Note: All ...
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The utility of HorsePower vs Torque

Which vehicle would experience greater acceleration (G) The acceleration is given by the force at the road. The force at the road is in turn specified by taking the power and dividing by the speed. ...
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How to find the direction of acceleration if an object is changing its direction of velocity but not magnitude then how we can find the direction

If velocity keeps the same magnitude at all times, then: $$\lVert\vec{v}\rVert=\text{cst} \quad\Rightarrow\quad \vec{v}.\vec{v}=\text{cst}$$ Derive this expression with respect to time: $$\vec{v}.\...
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4 votes

Can imaginary (illusionary) forces cause acceleration, and what exactly are they?

Fictitious forces seem to exist only from a Newtonian perspective: if we insist on thinking that the correct equation of motion is the Newton's second law: $$m\frac{\text{d}^2x^i}{\text{d}t^2} = F^i$$ ...
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-2 votes

Can imaginary (illusionary) forces cause acceleration, and what exactly are they?

The centrifugal force exist - it is the equal and opposite counterpart of the centripetal force. For example, imagine a ball attached to the end of a pencil with a string. Hold the pencil and spin ...
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Deriving normal acceleration in a uniform circular motion using limits

You're missing a square root: $\Delta v = \sqrt{ v^2+v^2-2vv\cos(\theta)}$. We can factor out $v^2$ to get $v\sqrt{2(1-\cos(\theta)}$. The Taylor series for $1-\cos(\theta)$ is $\frac{\theta^2}{2}-\...
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38 votes

Can imaginary (illusionary) forces cause acceleration, and what exactly are they?

The fictitious forces appear in non-inertial frames of reference. The forces can cause acceleration when viewed in such a frame. Riding in a car that swerves left, my coffee and donuts slide across ...
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2 votes
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What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?

The two kinematic equations for constant acceleration that you have quote are correct. If they are combined the error that you have made is revealed. Substituting for the acceleration $a= \dfrac {v-u}{...
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1 vote

What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?

this is because v is not equal to s/t. otherwise the equation of kinematic would be s=vt not s=ut+1/2 a t^2. you cant apply speed= distance/time unless you have constant acceleration
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What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?

You cannot calculate final velocity in your case as Distance / Time, this formula is only applicable to the movement with constant speed, or, to be more precise, it is calculating average speed.
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The meaning of negative sign in vectors?

By convention, the magnitude of a vector is always of a non-negative number. So for a vector $\vec{a} = (-5) \hat{\imath}$ the interpretation is as follows $$ \vec{a}\;\;\; = \underbrace{5}_\text{...
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2 votes
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The meaning of negative sign in vectors?

In rectangular coordinates, the general equation for the velocity (or any) vector is $$\vec v=v_{x}\hat i+v_{y}\hat j+v_{z}\hat k$$ where the values $v_x$, $v_y$ and $v_{z}$ are real numbers that can ...
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Special relativity and acceleration of an object falling in a direction perpendicular to the direction of motion

Imagine a train moving along a smooth surface with a velocity 0.98c along the x axis with respect to some observer on the surface. Imagine in the train's frame of reference (let's call it S2), an ...
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If An Instantaneous Force Causes A Charged Particle To Briefly Accelerate, Does Self-inductance Decelerate It?

The case of an accelerated charge gives rise to a disturbance in the field around that charge; that disturbance generates photons, called 'synchrotron radiation' because it is a major energy loss ...
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1 vote
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Special relativity and acceleration of an object falling in a direction perpendicular to the direction of motion

The disagreement is caused by combining Newtonian gravity with special relativity, which is not general relativity (GR). In weak GR (and 1g is weak) there is a graviomagnetic field that has a $\vec v/...
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Confusion regarding pseudo force

To (badly) quote Einstein, pseudo-forces are an ugly way to express the fact that the chosen frame isn't inertial. Say you're in a bus. As long as the bus goes in a straight line with constant ...
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1 vote

Confusion regarding pseudo force

Well, they accelerate to the same rate relative to what? Let say they both have acceleration a relative to an inertial frame. So in the inertial frame there must be a (real, not pseudo) force ...
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If An Instantaneous Force Causes A Charged Particle To Briefly Accelerate, Does Self-inductance Decelerate It?

The brief change in the magnetic field will cause a brief change in the electric field, which I think by Lenz’ law will be in the opposite direction of the particle’s velocity, slowing the particle ...
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If An Instantaneous Force Causes A Charged Particle To Briefly Accelerate, Does Self-inductance Decelerate It?

From Wikipedia Lenz's law states that: The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the ...
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Properties of inertial reference frames from different perspectives

Answer to a- the only force acting (as stated friction is not present)is weight of it and the body will have only acceleration due to gravity more accurately saying only have vertical component of ...
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Newton's Principle of Determinacy (intuitive explanation)

According to Arnold, the statement that says ``we don't need acceleration to predict the future'' is simply an experimental fact. Furthermore, it's said later in Arnold's book that positions and ...
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How do I get the velocity $v$ as a function of position $x$ from the acceleration $a$ as a function of velocity?

If acceleration $a$ is only a function of speed $v$ then the following equations are used to find distance and time $$ \begin{aligned} x - x_0 = \int_{v_0}^v \frac{v}{a}\,{\rm d}v \\ t - t_0 = \...
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How do I get the velocity $v$ as a function of position $x$ from the acceleration $a$ as a function of velocity?

From $a_x = dv_x/dt$, using the chain rule, we can write: $$a_x = \frac{dv}{dx}.\frac{dx}{dt} = \frac{dv}{dx}.v$$ And then, from the equation $a = f(v)$, $$f(v) = v.\frac{dv}{dx} \rightarrow \frac{v....
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2 votes
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Is this expert report wrong about basic kinematics?

You've misinterpreted the quote. The quote describes stopping distance, not stopping time. The distances are expressed as times at a certain starting speed. Context from the quote suggests that this ...
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2 votes
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What's the answer to this differential equation of a ball rolling in a semi-circle

The equation can be written as $$2r\int \frac{\mathrm{d}v}{2rg-v^2}=\int \mathrm{d}t$$ Now we can use the standard integral $$\int \frac{\mathrm{d}x}{a^2-x^2}=\frac{1}{2a}\ln\left(\frac{a+x}{a-x}\...
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