All Questions
Tagged with kinematics classical-mechanics
255 questions
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Why is the tangent of the rear wheel path of a bicycle parallel to the frame?
In "bicycle problems" (made famous for example by the book "Which Way Did the Bicycle Go?") the relevant point is the following: If $r(t)$ and $f(t)$ are the points of contact of ...
- 213
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1
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90
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Derivative of the product of a scalar function and a vector valued function
According to Berkeley Physics Course, Volume 1 Mechanics,
The time derivative of a vector valued function can be derived from the formula:
$$
\mathbf{r}(t) = r(t)\mathbf{\hat{r}}(t)
$$
where the ...
- 25
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2
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54
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The No Slip/Slip Condition for Rotating/Rotating and Translating Bodies
Consider a sphere of radius $r$ that is rolling on a rough surface, where its translational velocity $v$ is equal to $\omega r$, where $w$ is the angular velocity of its rotation. In this case, I ...
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Work Done by kinetic friction in Circular Motion
We know when an object is moving in a circular motion on a rough horizontal surface, direction of kinetic friction is constantly. Thus, fto calculate the work doen by friction, we need to use ...
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3
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
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21
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Position and displacement vector in Arc coordinate system
In Arc coordinate system the position of the particle is given by the length of the path(which is pre-determined and may also be curved) that it has travelled so how can we write it's position vector ...
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27
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How to mathematically model a lumped-mass cable model?
I am trying to simulate a 2D cable as a lumped-mass model. I think that it's like a chain of pendulums and I would preferably like to be damped. Just to make sure, this is the cable model that I'm ...
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Why don't they use golf ball dimples on bullets or cannon balls? [duplicate]
Dimples help the golf ball to fly far. But do you know why they don't use them on bullets or cannon balls?
Some kinds of cannon ball have similar size as a golf ball.
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4
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213
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Why acceleration is not always parallel to velocity but velocity is always parallel to displacement? [closed]
Velocity is derivative of displacement :
$$\vec v=\frac{\mathrm {d\vec r}}{\mathrm dt}$$
And acceleration is derivative of velocity.
$$\vec a=\frac{\mathrm {d\vec v}}{\mathrm dt}$$
Given that their ...
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Absolute Angular Velocity - How to use?
From my dynamics course, we were introduced to the so-called absolute angular velocity of a rigid body. Below is a short diagram:
The following equation for the velocity of point P on a rigid body is ...
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4
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100
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Understanding velocity as a vector quantity [closed]
Why is velocity classified as a vector quantity. Can it be explained by the same way as force referring to the Phys.SE post Where am I confused about force addition?
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3
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How do you prove the formula for momentum? [closed]
I am just an absolute beginner to physics. I've seen a proof of the formula for momentum using Newton's second law of motion, but to prove Newton's second law of motion you have to use the formula for ...
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1
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92
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Why isn't work $Fd \sec \theta$? [closed]
In the following image if force the triangle PAN was right angle at P then the component of force in the direction of displacement would be $F\sec\theta$ so work $F*Displacement(AC)*\sec \theta $.
I ...
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6
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226
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How to determine whether an object is a point object?
I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks ...
user366132
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Equation of Motion of Rigid Body Represented by Twist and Derivative of Twist
This question is an extension of question Understanding terms Twist and Wrench.
Assuming there is a rigid body with body twist denoted as $\mathcal{V}_{b}=\left(\boldsymbol \omega_{b}, \boldsymbol v_{...
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166
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Why is the ratio of components of kinetic energy equal to the ratio of kinetic energy to total energy for a projectile whose range is maximized?
The launch angle $\theta$ that maximizes the range of a projectile in a uniform gravitational field is
\begin{align}
\theta = \arctan\left(\frac{v_o}{\sqrt{v_o^2 + 2gh}}\right), \tag{1}
\end{align}
...
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1
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1
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182
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Bouncing a ball on an elevator that is ascending
My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises ...
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3
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1
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302
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Relation between "method of moving frames", spin connection, Cartan forms, and classic rotational kinematics in $\mathbb{E}^n$
I want to know how the "method of moving frames" involving things like connection 1-forms, torsion 2-forms, spin connections, etc. are applied to basic rotational kinematics in flat 3-space (...
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2
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55
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Is the way of determining my angle of vector wrong or am I using the wrong formula for calculating magnitude of resultant? [closed]
i) Two balls A and B are simultaneously projected from top of building at 10m/s upward and 20m/s downward. Find distance between them after 3s? (Answer: 90m)
There are two magnitude of resultant ...
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1
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94
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Velocity and acceleration of a ball shot uphill [closed]
Consider a ramp of length $100$ m and with a height of $10$ m. At the base of that ramp we're shooting a ball of mass $12$ kg uphill. Let's say the ball has a speed of $1$ m/s at $1$ m uphill. How can ...
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3
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2
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197
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Physical meaning of $dx/dt$ for objects of changing length
I was solving '200 Puzzling Problems in Physics' as a recreational activity and I encountered this beautiful question which surprised me as I understood a basic flaw in my conceptual understanding.
...
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Do released objects take the direction and speed of their parent frame's velocity, or just the parent frame's speed component?
Context: I'm working on a space game. I noticed that an unpowered object fired from a strafing spaceship appeared, as the released object moved, to curve in the direction the ship was strafing. This ...
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1
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Elastic potential energy in vertical simple harmonic motion
When we calculate gravitational potential energy, we use a reference point as a zero-line. That is, we set the gravitational potential energy to zero at a specific point (usually the ground). Now, ...
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1
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60
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Conceptual difficulty with with component accelerations in polar coordinates
In kinematics why is the acceleration along the radius not the time derivative of the velocity along that radius?
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1
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138
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Question about period and frequency
In the context of uniform circular motion, I have been so informed that period ($\tau$) is properly measured in seconds; and that frequency ($f$) in inverse seconds. Why is this the case? Wouldn't the ...
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1
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97
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Angle, and maximum area of projectile motion accounting air resistance
Recently I was wondering about what will happen to the particle when subjected various elevation angle of projectile motion if we account air resistance. I want to know what the angle of elevation ...
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31
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What was the professor counting regarding constraint forces? [duplicate]
I am taking a mechanics class at university. Last week we started describing movement over a curve; we are given a natural parametrisation $s(t)$, and then we have the following relations:
$$ \vec{r}(...
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2
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2
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281
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When a car curves, if friction points towards the centre which force makes the wheel rotate?
The translational motion of the wheel is due to the friction right. If friction is towards the centre during a turn, which provides the translational motion to the wheels? Or is it the component of ...
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110
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Trajectory of particle thrown from the center of rotating frame of reference
So we have a rotating platform with two frames o reference: the one which is static, $O:\{x,y,z\}$, and the one wich is rotating along the platform, $O':\{x',y',z'\}\ (z\equiv z')$. The platform is ...
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71
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Relation between fixed constraints and time derivative of the Lagrangian
I have had some trouble interpreting and proving the following statement from Fasano, Marmi's "Analytical Mechanics" (page 139):
"... ${\partial L}/{\partial t} \neq 0$ (1) only if the ...
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0
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44
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Violation of conservation of energy [duplicate]
Sand runs from a hopper at a constant rate $\frac{dm}{dt}$ onto a horizontal conveyer belt driven at a constant speed $v$ by a motor. The power needed to drive the belt can be calculated as follows:
...
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1
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1
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63
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Determining the trajectory of a particle given the tangential and normal accelerations
Consider a particle with tangential and normal accelerations $\vec{a_T}(t)$ and $\vec{a_N}(t)$ respectively ($t$ is time). If the initial velocity and position vectors are both $\vec{0}$, how can the ...
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0
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29
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Explicit Example of Computing the Action [closed]
I have been dealing with this problem for awhile and I have almost given up. I am asked to compute the action for a free particle going from $x = x_0 = 0$ at time $t = t_0=0$ to its end point $x = x_1 ...
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2
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239
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Angle of projection for the minimum time of flight for a given range
If a projectile has to cover a fixed range under gravity, then what should be the angle of projection for the total time of flight to be minimum?
The initial and final point of the projectile are both ...
2
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3
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436
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Can something have momentum but not velocity?
The idea of momentum is fundamental, even more fundamental than velocity or mass. But I was wondering can momentum exist without velocity, since momentum can exist without needing mass?
Thinking ...
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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
I am new at this topic so please do mind if my question doest make sense to you.I am trying to find out that what will be the direction of acceleration if object changes Direction of velocity but not ...
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0
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73
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Necessary and sufficient conditions for periodic motion
Let us fix a reference frame $S$ with origin in $O$ in the euclidean space $\Bbb R^3$, then let us also define a periodic motion in the following manner:
A motion is periodic if and only if the time-...
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2
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1
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93
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Car moving on a ball in space
Consider a car of mass $m$ moving on the surface of a ball (think of it as earth) with moment of inertia $I$, floating in a vacuum.
Let the car slowly (adiabatically) drive around the circle of ...
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2
answers
60
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When does a free body moving on a smooth circular path make a complete revolution?
If we have a body like the one below , What will be the minimum initial velocity $V_0$ to complete one revolution, My assumption was that it has to reach $\theta=180$ ,But how do I describe this ...
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2
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434
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula
My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step.
How do you derive the ...
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2
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45
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Can a frame still be an inertial frame if its center varies with time relative to a “true” inertial frame?
Picture a seat on a Ferris wheel. Neglecting any rocking, is the seat of a Ferris wheel an inertial frame?
My guess is that yes it is right? The frame itself isn’t rotating or accelerating relative to ...
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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 ...
1
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2
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461
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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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1
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87
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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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1
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1
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450
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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?
This question is highly related to working with the ...
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3
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1
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242
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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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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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1
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1
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55
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Relating speed of a flywheel to speed of a shot-out ring [closed]
Let's say I was shooting a 6 lb/cu ft foam ring with an inside diameter of 3 inches and an outside diameter of 5 inches using a flywheel like this:
where s is the distance between the wall on the ...
2
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2
answers
284
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Acceleration without a force in special relativity
Let us consider a relativistic particle of mass $m$ and charge $q$ in a constant electric field $\mathbf{E}=E\mathbf{\hat{j}}$ moving in two spatial dimensions, a relativistic extension of the well-...
- 1,112
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1
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71
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An easier way for me to calculate the distance , But does it always stand true? [closed]
When can I say that the distance is equal to $d=\int^{t_2}_{t_1}|V|dt$ , Where V is the velocity and it's given in terms of time and $t$ is the time , You might wonder why I'd need this ; it's ...
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