Aparticle of mass m moves along the r-axis under the influence of a time- dependent force given by fr, t) = -kret/7, where k and 7 are positive constants. (a) compute the lagrangian function. [7 points) (b) find the lagrangian equation of motion explicitly. (7 points) (c) compute the hamiltonian function in terms of the generalized coordinate and generalized momentum. (show clearly how you got this.) (7 points] (d) determine hamilton's equations of motion explicitly for this particular problem (not just general formulae). [7 points) (e) does the hamiltonian equal the total energy of the mass? explain. [6 points) (f) is the total energy of the mass conserved?

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.