3
votes
3answers
137 views

Explanation of line element formula $dl^2 = dx^2 + dy^2$

I found this in a physics textbook without justification: $$dl^2 = dx^2 +dy^2,$$ where I presume that $l = \sqrt{x^2+y^2}$. Why is this so? By my calculations I obtain $$ dl = \dfrac{\partial ...
0
votes
1answer
77 views

I can't seem to find this derivative any help would be great.

A rocket of mass m = 1000 kg is traveling in a straight line for a short time. The distance in meters covered by the rocket during this time is described by the function $r(t)=t^3 −3t^2 +6t$ where ...
0
votes
2answers
62 views

Proof that energy of a free body is constant, using the derivate

Ok, what I'm trying to prove is the law of conservation of energy for a free fall. Let the downward direction be positive. We want to prove that: $$mgh+\frac{mv^2}{2}=constant$$ For this, we try to ...
0
votes
2answers
39 views

Calculate the energy in a circuit containing a resistor

A voltage peak in a circuit is caused by a current through a resistor. The energy E which is dissipated by the resistor is: Calculate E if Can anyone please give me some suggestions where to ...
0
votes
2answers
25 views

Find the units of measurement of constant from formula

$$m\frac{dv}{dt}=mg-kv^2$$ $v=\ms^{-1} $m=kg$ $g=ms^{-2}$ $v^2=(ms^{-1})^2 I re-arrange the formula to isolate K $$K=-\frac{m\frac{dv}{dt}}{v^2}+\frac{mg}{v^2}$$ Sub in the units ...
0
votes
1answer
25 views

Finding units of measurement of coefficients in ODE's

If we have a question where we have to find the coefficient's units such as K in this case. The actual formula contains more parts but it is simply the derivatives that I am unsure about. ...
1
vote
1answer
85 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
214 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
58 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
103 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
47 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
41 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
23 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
846 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
6k 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
216 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
75 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
84 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
129 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
435 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
213 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
379 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
160 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
54 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
1k 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
124 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
53 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
469 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 = ...
4
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: $$ ...