Find the time that a force of 38.5 N acted on a 12.0 Kg object moving to the right to change its speed from rest to 25.3 m/s.

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.

You are a sales representative for a company that makes a new alternate fuel for vehicles. you have prepared a presentation for the environmental engineers to sell your new product. what question do you expect the audience to ask regarding whether the new fuel will cause less damage to the environment? a. do we have to change any parts of the vehicle to use this alternate fuel? b. will the vehicles get better fuel mileage with the alternate fuel? c. how much greenhouse gas does your fuel produce compared with current fuel sources? d. is the alternate fuel more expensive than fossil fuel?

An electron is ejected into a horizontal uniform e⃗ field at a parallel horizontal velocity of v0. assume the electron's initial position x0, initial velocity v0, time t, magnitude of electric field e, electron's mass m, and the magnitude of the electron's charge |e|. ignore the force that earth exerts on the electron. assume the e⃗ field is in the same direction as the initial velocity. part a define the equation for the electron's velocity. express your answer in terms of the variables v0, |e|, t, e, and m.