# Tag Info

Accepted

### Why do we need instantaneous speed?

Because instantaneous speed affects physics. Imagine a wall $10~\textrm m$ in front of you. You walk towards it smoothly over a timeframe of, say, $20~\textrm s$, and without getting slower, you walk ...
• 2,703
Accepted

### How is it possible to differentiate or integrate with respect to discrete time or space?

Let's say space is really a lattice with spacing $\Delta x$. It turns out that this idea has more trouble with experiment than you might think, but we can plow ahead for the purposes of this question. ...
• 52.3k

### Does it make sense to take an infinitesimal volume of shape other than a cube?

Infinitesimal volume elements do not have to be cubes. Some familiar examples come from typical solids of revolution problems from calculus 1/2. Typically one discusses using either the "disk/...
• 58.2k

### Why use Fourier series instead of Taylor?

The complex exponentials are eigenfunctions of the derivative and integral operators. So if you're analyzing linear differential equations, and using Fourier series, then you can consider each term on ...
• 28.8k

### How does instantaneous velocity or acceleration have any other numerical value than 0?

Suppose you are travelling at a uniform velocity and you cover 1 meter in 1 second. Your average velocity is $$\frac{1\ {\rm m}}{1\ {\rm s}} = 1 \frac{\rm m}{\rm s}.$$ If you consider a 1 ...
• 28.8k

### What's the difference between average velocity and instantaneous velocity?

Your question is legitimate and I don't understand why it got downvoted. The confusion arises in the difference between average and instantaneous velocity. Consider this example: a car moves at 10 m/...
• 4,746
Accepted

### How does instantaneous velocity or acceleration have any other numerical value than 0?

$$v_\text{average}=\frac{\Delta s}{\Delta t}$$ $$v_\text{instantaneous}=\lim_{\Delta t\to0}\frac{\Delta s}{\Delta t}$$ If the time interval gets infinitesimally small $\Delta t\to 0$, then you are ...
• 51.7k
Accepted

• 40.3k

### Why do we need instantaneous speed?

It is really simple: Average speed is as good as instantaneous speed only if speed does not change with time. If you are studying a body with rapidly changing speed then using average speed to ...
• 4,565

### Explaining how we cannot account for changing acceleration questions without calculus

You do, in fact, have to take into account the change in separation distance between charged objects when analyzing the dynamics of the system. This is done mathematically through the use of ...
• 1,004
Accepted

### When the direction of a movement changes, is the object at rest at some time?

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. ...
• 75.6k
Accepted

• 917

### Explaining how we cannot account for changing acceleration questions without calculus

On a historical note, Isaac Newton studied the same problem for gravity, and presented the solution in Principia Mathematica without using calculus, although it turns out that he had privately ...

### Can $d/t =$ speed ever be wrong? Is there a more accurate way to determine speed?

I'm very sorry for your loss. The definition of the average speed of an object as it passes between two points is the distance $d$ between them divided by the time $t$ it took to get from one to the ...
• 70.5k

### How area under Velocity-Time graph represents magnitude of displacement?

Imagine dividing your graph of velocity vs. time into a bunch of extremely thin vertical rectangles. It's reasonable to say that, over such a short time, velocity is constant in any given rectangle. ...
• 35.7k

### Question about derivation of kinematics equations

Given velocity $v(t)$, the distance moved after a certain time $t$ is not $v(t)t$ - this formula works at constant velocity, but when the velocity is changing, the correct expression is \$\int^{t_f}_{...
• 21.6k

### How is it possible to differentiate or integrate with respect to discrete time or space?

This is a comment, as Andrew's answer is adequate for the problem. I want to point out , which is not clear in your question, the difference between mathematical modeling and the object modeled. When ...
• 235k
Average speed is defined as passed-distance-over-passed-time: $$v_\text{average}=\frac{\Delta s}{\Delta t}.$$ In other words, choose a point on your path. Then choose one more point. Plug in the ...