1
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1answer
67 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
0
votes
1answer
85 views

Find acceleration at the first instant when a car has zero velocity.

The position of the front bumper of a test car under microprocessor control is given by: $x(t)=2.17m+\left(4.8\frac{m}{s^2}\right)t^2-\left(.100\frac{m}{s^6}\right)t^6$ Find its acceleration at the ...
1
vote
1answer
49 views

Starting velocity by distance, time, and friction

I am writing a game in Javascript, and I just got a big math problem, where $\text{friction} = 0.97$. This is what is being looped every $1000$ / $60$ milliseconds, to make the projectile move all ...
0
votes
3answers
64 views

Finding velocity in optimization problem

Given $s=-16t^2+192t+144$, what is the velocity when $s=0$? This is part of a larger optimization problem which I solved, except for this last part. The critical point occurs at $t=6$, so after ...
0
votes
1answer
37 views

Vector functions and motion along a curve

A particle moves along the curve $x=\ln y$ with a constant speed of $4$ units per second. Find the normal scalar component of acceleration as a function of $x$. Honestly, what I don't understand ...
1
vote
1answer
29 views

Deriving time and distance

The distance an aircraft travels along a runway before takeoff is given by $D=(10/9)t^2$, where $D$ is measured in meters form the starting point and $t$ is measured in seconds from the time the ...
0
votes
1answer
22 views

What does the result of derivating out all of the units from a “number” tell you?

I apologize for the terrible title, I'm not sure of the right way to say it. Consider an equation which outputs in Watts $ \frac{kg \cdot m^2}{s^3} $. If you derivative out all the changes in ...
0
votes
2answers
552 views

Find the position of the object when the velocity is 0

The position of an object given by $f(t)=5t^2-6t+13$ where $t$ is measured in seconds and the position is measured in meters. Find the position of the object when the velocity is 0. I'm confused on ...
0
votes
3answers
4k views

Derivation of Newton's second law of motion. [closed]

Can somebody help me determine the derivative and proof of Isaac Newton's second law of motion ($F=ma$)? How can this be done using calculus?
1
vote
1answer
131 views

Higher Derivatives of trigonometric functions

The position of a particle is given by $s = 5 \cos (2t+ (\pi/4))$ at time $t$ . What are the maximum values of the displacement,the velocity,and the acceleration? The answers are displacement: $5$ ...
2
votes
1answer
70 views

Find force required for a launch between two points

Let me start by saying this is within a game environment, so gravity isn't 9.81m/s^2, and the unit of measure for distance will be "blocks". I'm attempting to find the amount of force needed in order ...
2
votes
1answer
78 views

Time, Velocity and Acceleration

I'm working through some exercises and have again come across one that is giving me some trouble. The topic is calculating velocity and acceleration when time varies. Here it is: A body moves in such ...
2
votes
4answers
124 views

How can you show that $\delta′=f(0)\delta′−f′(0)\delta$ for a function f that is infinitely differentiable?

Assume that $f$ is infinitely differentiable. Let $\delta$ be the (Dirac) delta functional. I know that $f\delta = f(0)\delta$, but I'm not sure how to derive the equation ...
4
votes
1answer
373 views

Derivative of a bra?

I understand that $$ \frac{\mathrm d}{\mathrm dt} \langle\psi|\psi\rangle =\left[\frac{\mathrm d}{\mathrm dt} \langle\psi|\right]|\psi\rangle + \langle\psi|\left[\frac{\mathrm d}{\mathrm ...
1
vote
2answers
191 views

How to get the derivative of a physical formula?

I've heard that if $U_{ind} \neq $ constant, you must use the following formula: $ U_{ind} = N \times \dfrac{d \phi}{dt}$ I however don't know how to get the derivative of this formula? In math I ...
1
vote
1answer
367 views

Finding the initial velocity using calculus

I throw a stone at 20 degree, when the stone falls to the ground, it reaches 100m further. Using CALCULUS methods, find the initial velocity of the stone.
1
vote
1answer
140 views

The material derivative

Let $u:S(t) \to \mathbb{R}$ be a scalar field on a surface $S(t)$ parametrised by time. The material derivative is $$Du = u_t + v \cdot \nabla u$$ where $v$ is the velocity. I fail to understand the ...
-1
votes
0answers
53 views

Show the negative derivative [duplicate]

Possible Duplicate: Show the negative derivative of a function. A type of interaction between atoms in a molecule is called a Van der Waals interaction. This can be described by the ...
1
vote
4answers
974 views

Show the negative derivative of a function.

A type of interaction between atoms in a molecule is called a Van der Waals interaction. This can be described by the potential energy function; $$U= ...
1
vote
3answers
119 views

Help with odd partial derivatives in velocity $\bar v^2 = \dot x ^2+\dot y^2$

I am doing a physics -course Tfy-0.2061. My teacher claims that this is velocity squared, $\bar v^2 = \dot x ^2+\dot y^2$. I cannot understand why it is not $\bar v^2 = (\dot x +\dot y)^2$. If ...
0
votes
0answers
52 views

When can I treat vectors as regular variables when differentiating?

Given this Lagrangian where $\dot{\vec r} = \left(\dot x, \dot y, \dot z\right)^T$: $$ L = \frac m2 \left|\dot{\vec r}\right|^2 - q \left( \phi - \left\langle \dot{\vec r}, \vec A \right\rangle ...
1
vote
3answers
2k views

Velocity Question & Acceleration

Below I have a question that I tried to solve on a exam. I am curious as to the actual way to approach the question. What I did was set the equation equal to $0$ and get $t = -3$ then I plugged in $3$ ...
1
vote
1answer
427 views

del operator - partial derivatives

I'm taking a class in Electromagnetism, and I'm learning about the relationships between voltage and an electric field from Faraday-Maxwell equations. The equation I have trouble with is: $$E = ...
3
votes
4answers
3k views

Which of these two ways to take the derivative of a delta function times another function is correct?

A well known identity of the Dirac delta function is that for any function $f(x)$: $$ \delta(x) f(x) = \delta(x) f(0). $$ If we take the derivative of the right hand side we get: $$ ...