if u look at the velocity function then u will find that the velocity is negative in the time interval from "0 to sq.root(2/3) sec".

A particle of mass $40$ kg moves in a straight line such that the force (in newtons) acting on it at time ...

A particle usually speeds up when the velocity and the acceleration have the same signs. It slows down when the acceleration and velocity signs are different. My advice (even though it might take a while) would be to sketch the curve from the given function. Then, you can find where the particle speeds up and slows down.

Set up the Lagrange equations of the first kind and determine the constraint force and the point at which the particle detaches from the hemisphere as well as its velocity at that point. Set up the Lagrange equations of the first kind for polar coordinates and find the angle and angular velocity at which the particle detaches.

Aug 19, 2017 · Suppose I have set of samples $(x_i,y_i), 1 \leq i \leq n$. I am interested in solving the following optimization problem: $$ \min \sum_{i=1}^n (y_i-a^\top x_i)^2 ...

Multivariate Taylor series is used in different optimization techniques; that is you approximate your function as a series of linear or quadratic forms, and then successively iterate on them to find the optimal value.

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Oct 16, 2015 · The space between "arg" and "min" is confusing; it would better be written "argmin". What the operator argmin does, when applied to a function, is pick out the point in the function's domain at which the function takes its minimum value (assuming that …

Oct 28, 2015 · In fact, on P. 51 Borisenko and Tarapov show that if the force is everywhere tangent to the curve of travel, then the particle will travel in a straight line as well. Again, even if there is a force on it, as long as the force does not have a component perpendicular to the path, a particle will travel in a straight line between two points.

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