Leslie is speeding up to merge with traffic. When she begins to speed up, she has a velocity of 7.0 m/s west. When she merges with traffic 7.0 seconds later, she is traveling 23 m/s. Assuming east to be the positive direction, what is Leslie’s average rate of acceleration during this period? Select one:

a.2.3 m/s ^{2}

b.1.9 m/s ^{2}

c. -1.9 m/s ^{2}

d.-2.3 m/s ^{2}

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.

An object weigh 40n in air ,weigh 20n when submerged in water,and 30n when submerged in a liquid of unknown liquid density.what is the density of unknown of liquid?

Aprotein molecule in an electrophoresis gel has a negative charge. the exact charge depends on the ph of the solution, but 30 excess electrons is typical. what is the magnitude of the electric force on a protein with this charge in a 1600n/c electric field? write in two significant numbers, and also in newton