What is the average velocity of the object between 14 and 22 seconds

When you drop a pebble from height a it reaches the ground with speed v if there is no air resistance. from what height should you drop it so it will reach the ground with three times the speed? (a) 9m (b) 3m (c) 6m (d) 18m

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.

The combining of light nuclei is called blank. blank as in not actually blank. you know what im tryin to say.