Aparticle slides frictionlessly along a path in a vertical plane from point a to a lower point b under the force of gravity. the brachistochrone problem is to find the path that gives the minimum travel time when the particle starts from rest at a. find a solution for the path. you can take point a to be the origin of your coordinate system hint: you should find that you need to evaluate an integral of form v2 dy, where a is a constant. make the substitution y = a(1-cos θ). this will allow you to find a parametric solution for the minimum time path in terms of θ

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explanation:

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

myth. it was once thought that animals, including cats and dogs, could only see in black and white. however, scientists have proven this to be a myth. in all animals, including humans, the perception of colour is determined by the presence of cells in the eye called cone photoreceptors.