Which of the following quantities are physically "equal" in Newtonian mechanics? a. Energy and Power b. Power and Work c. Work and energy d. Mass and energy e. Mass and acceleration f. None of the above.

Solve correctly in 20 minutes. Will give upvote.

4. A lkg mass initially at rest is accelerated by a 30N force, continuously, for a full year. How fast is it going at the end of that year? (If your answer is larger than the speed of light, you've done something wrong!). Hint: F = Ap/At.

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 F: (a) Using Newton's second law, show that d -mx². dt GmM x² i. GmM X = 0. dv dv (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables var dr, solve the equation of motion and determine the = dx 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 O depend on the initial position? dt' =