When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose magnitude is k/x2. If the particle starts from rest at x = b and is acted on by no other forces, find the work done on it by the time it reaches x = a, 0< a< b.

Q: A particle's position at time tis given by r(t)= (3t",4t+1,-t). Find a, att=3.

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Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

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Q: An object travels in a straight line with velocity v(t) = 6 − 3t over the timeinterval [0, 5]. Find…

A: We first find the t intercept of v(t)=6-3t  for that, we plug v(t)=0 and solve for t For t&lt;2 ,…

Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: Find the work done for a force F=36/x^2 N from x =1 to x=6 m.

A: The objective of this question is to calculate the work done by a force that varies with position.…

Q: A mass of 3 kg is suspended from a spring whose constant is 2 Nt/cm. The system is then immersed in…

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Q: A particle moves along an s-axis with the acceleration function 15 a(t) = Vt + 6t - 4 Moreover, its…

A: The acceleration function of a particle,at=154t+6t

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.