What is terminal velocity derive?
Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. It is observed when the sum of drag force and buoyancy is equal to the downward gravity force acting on the object. The acceleration of the object is zero as the net force acting on the object is zero.
What is the differential equation of velocity?
For example, if y is the height above ground of a falling object then the first-order derivative y ‘ is the object’s velocity and the second derivative y ” is its acceleration. The equation y ” = k is a second-order differential equation that represents the movement of an object that has constant acceleration k.
What is Stokes law and terminal velocity?
In Stokes’s law, the drag force F acting upward in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall.
What is the formula of terminal velocity Class 11?
Terminal velocity is attained when Force of resistance = force due to gravitational attraction. 6πηrv = densityxVg (Because density=m/V), density=ρ – σ where ρ and σ are the densities of the sphere and the viscous medium resp.
How do you calculate differential equations?
Steps
- Substitute y = uv, and.
- Factor the parts involving v.
- Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
- Solve using separation of variables to find u.
- Substitute u back into the equation we got at step 2.
- Solve that to find v.
What is differential velocity?
If position is given by a function p(x), then the velocity is the first derivative of that function, and the acceleration is the second derivative. By using differential equations with either velocity or acceleration, it is possible to find position and velocity functions from a known acceleration.
What is a differential equation simple?
Definition: differential equation. A differential equation is an equation involving an unknown function y=f(x) and one or more of its derivatives. A solution to a differential equation is a function y=f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation.
What exactly is differential equation?
Differential equations are equations that relate a function with one or more of its derivatives. This means their solution is a function!
How do you create a differential equation?
Step 1: Differentiate the given function w.r.t to the independent variable present in the equation. Step 2: Keep differentiating times in such a way that (n+1) equations are obtained. Step 3: Using the (n+1) equations obtained, eliminate the constants (c1 , c2 … ….
What is terminal velocity class 11th?
Terminal velocity is the maximum velocity of a body moving through a viscous fluid. It is attained when force of resistance of the medium is equal and opposite to the force of gravity.