An object is at x = 0 at t = 0 and moves along the x axis according to the velocity–time graph in figure p2.50.(a) what is the object’s acceleration between 0 and 4.0 s? (b) what is the object’s acceleration between 4.0 s and 9.0 s? (c) what is the object’s acceleration between 13.0 s and 18.0 s? (d) at what time(s) is the object moving with the lowest speed? (e) at what time is the object farthest from x = 0? (f) what is the final position x of the object at t = 18.0 s? (g) through what total distance has the object moved between t = 0 and t = 18.0 s?

What is work? how much work is done to move an object 0 meters?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Consider a system with two masses that are moving away from each other. why will the kinetic energy differ if the frame of reference is a stationary observer or one of the masses?