Velocity, then, is the rate of change or slope of position. By the same token, acceleration is the rate of change or slope of velocity. In fact, calculus grew from some problems that European mathematicians were working on during the seventeenth century: general slope, or tangent line ...
Set the initial conditions for the oscillation amplitude as x(0)=10 and the initial velocity of the mass as ˙x(0)=0. Get assume(m,'positive') assume(k,'positive') Dx(t) = diff(x(t),t); xSol = dsolve(eqn,[x(0) == 10, Dx(0) == 0]) xSol = 10 cos(√k t...
Z. Guo,S. Gala.A regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity field. . 2010S. Gala, M. A. Ragusa, On the regularity criterion for the Navier-Stokes equations in terms of one directional derivative, Asian-Eur. J. Math. 10(...
[esp. Brit.,]differential coefficient.the limit of the ratio of the increment of a function to the increment of a variable in it, as the latter tends to 0; the instantaneous change of one quantity with respect to another, as velocity, which is the instantaneous change of distance with res...
For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is traveling. Conversely, the integral of the velocity over time is the vehicle's position.The derivative of a ...
What are derivatives used for? Derivatives are used to find the value of instantaneous rates of change of a given function. If you know a function for the distance a particle traveled, for instance, the derivative will tell you the velocity of that particle at a specific time.First...
The derivative of velocity with respect to a coordinate Why ##\frac{\partial (0.5*m*\dot{x}^2-m*g*x)}{\partial x}=-mg##? why ##\frac{\partial \dot{x}}{\partial x}=0##? Why ##\frac{\partial (0.5*m*\dot{x}^2-m*g*x)}{\partial \dot{x}}=m*\dot{x}## ? why ...
go around bends, climb hills, and descend declines. We might formulate a function for distance traveled that involves additional variables, such as altitude. That function would incorporate both time and altitude, and we can take the partial derivative of that function with respect to either altitu...
In this paper, we consider the conditional regularity of weak solution to the 3D Navier–Stokes equations. More precisely, we prove that if one directional derivative of velocity, say ∂3u, satisfies ∂3u∈Lp0,1(0,T;Lq0(R3)) with 2p0+3q0=2 and 32<q0<+∞, then the weak solution...
Defining the Derivative of a Function and Using Derivative Notation->Differentiation: Definition and Basic Derivative Rules The velocity v, in meters per second, of a certain type of wave is given by v(h)=3 √(h), where h is the depth, in meters, of the water through which the wave ...