So d 2 v/dt 2 is a small change in acceleration with respect to time. (I think that's called jerk in physics, but we seldom use it.) Also, dv/dt is really just a fancy way of saying d 2 x/dt 2 because v = dx/dt -- that is, speed = change in distance over change in time.

Since a a is defined as the rate of change of velocity with respect to time: a = dv dt a = d v d t , and is identical to a = dv dt. dx dx a = d v d t. d x d x where dx dt d x d t is velocity, then we are left with:

2017年4月4日 · When $\\hat T$ is the unit vector that is tangent to a $\\vec r$ vector that describes a particle's movement in space we can write the velocity vector as: $$\\vec v=v*\\hat T$$ Then if we take the deri...

2015年9月16日 · How to solve this differential equation: $$ m* (dv/dt)=-m g- r v$$ where m, r and g are constants. I am trying to rewrite the equation as dv=dt form, but I do not know how to do it.

2018年9月28日 · The expression amounts to saying that " the change in velocity per unit of time [dv/dt] equals the change in velocity per unit of distance [dv/dx] times the change in distance per unit of time " [dx/dt]. Imagine moving along a ruler with very fine markings (e.g. one marking for each micrometer) while timing the movement with a very finely divided clock (ticking once each microsecond, for ...

2022年2月1日 · When you see dv/dt = a (t) that indicates first time derivative of velocity to get you acceleration as a function of time, which is great if acceleration is changing with time. v/t=a typically will give you an *average* acceleration. As sonnyfab said, this will get you the same results *if* acceleration is constant through the whole time frame.

2015年7月31日 · Water evaporates from an open bowl of unspecified shape at a rate proportional to the area ofthe water surface; that is, $$\\frac{dV}{dt} = -cA(h)$$ where V is the volume of water, A(h) is the area ...

I'm working on some mechanics at the moment and can across this issue in a question. Distance differentiated in regards to time becomes velocity: dx/dt d x / d t. Differentiate velocity in regards to time and you get acceleration: d2x/dt2 d 2 x / d t 2. If I have v2 v 2 and want to differentiate in regards to time, how would you go about doing so?

Or else "The change in volume (dV) with respect to time (/dt)". This means that for every time increment, volume is changing at whatever rate. So many meters or centimeters cubed per minute or second are being added or subtracted from the volume. It is the same with d/dt but that is general. So d/dt is just general change of each variable over ...

2023年5月2日 · @JohnDouma Written as the chain rule, it would be d dtv(x) = dv dxdx dt d d t v (x) = d v d x d x d t. Doesn't the existence of dv / dx d v / d x presuppose that velocity can be written as a function of position? Is that true? For example, with a parabolic trajectory, one value of the position can correspond to multiple values of velocity.