Sep 16, 2015 · To "look" inside your interval you can reduce the time interval and try to focus on a specific instant. This means reducing Δt to zero or at least tend to zero! So, basically, you'll be able to evaluate the velocity at a point (not interval) and have an instantaneous velocity!

Sep 28, 2018 · The change in velocity of the pie as it's traveling through space to your friend's beautiful face (dv/dx) is a factor of the change in space between the pie and your friend's face within the 2 seconds (dx/dt).

Apr 12, 2017 · $$v=\frac{dx}{dt}=-gt+v(0)\tag{2}$$ where $v(0)$ is the velocity at time $t=0$. If the object was merely dropped from some initial height $x(0)$, then $v(0)=0$.

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Sep 16, 2014 · What is the formal explication of the fact that $dx/dt = v(x)$ implies that $dt/dx=1/v(x)$? Is that via geometry? analysis? differentiable forms? Can you give me reasons for that?

Dec 1, 2019 · Yes, you can write v as a function of x, but only on the basis that the relation x=x (t) can be inverted. E.g. if x=f (t) and v=g (t) then t=f -1 (x), so v=g (f -1 (x)). The equation applies where f is a function of two independent variables, x and y.

$a=\frac{dv}{dt}$, and is identical to $a=\frac{dv}{dt} .\frac{dx}{dx}$ where $\frac{dx}{dt}$ is velocity, then we are left with: $$a=v\frac{dv}{dx}$$

Jul 5, 2005 · In general, dx/dt represents the rate of change of position with respect to time, while dv represents the rate of change of velocity with respect to time. If we are dealing with a constant velocity, then dx/dt and dv would be the same, as the velocity is not changing.

From the definitions: v = (ds/dt) and a = (dv/dt) it is seen that dt = (ds/v) = (dv/a) so that v dv= a ds. Integrating this expression for motion between locations s = 0 and s gives: v (t)2 = v (0)2 + 2as.

This means that the velocity over a certain period of time is the instantaneous change in position (dx) over the instantaneous change in time (dt) . This period of time is intentionally very small, hence "instantaneous".