H2 pls H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimensionunder the influence of the gravitational force of another point particle of constant mass Msitting at x = 0, i.e. the attracting force isF=(a) Using Newton's second law, show thatd (2m²² -dtGmMGmMi.= 0.(i.e., the total energy, sum of kinetic and potential energy, is conserved).(b) Using the change of variables v=d, solve the equation of motion and determine thevelocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Doesthe particle's speed in x = 0 depend on the initial position?X

We will answer the question by substituting the given force in Newton's second law and…

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is GmM X² -i. F= (a) Using Newton's second law, show that d a ( 12m² __ GmM) = dt = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables v , solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position?

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is GmM X² -i. F= (a) Using Newton's second law, show that d a ( 12m² __ GmM) = dt = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables v , solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position?