The equation for the acceleration of a body moving in a circle is , where a is acceleration, v is velocity and r is the radius of the circle. acceleration has units of m/.

a. what is the acceleration of a body moving with a velocity of 30 m/s in a circle of radius 10 m?

b. solve the equation for velocity

c. what is the velocity of a body that has an acceleration of 20 m/ and is moving in a circle of radius 2 m?

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.

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

One number is said to be an "order of magnitude" larger than another number if choose one: a. it is 10 times larger. b. it is 5 times larger. c. it is 3 times larger. d. it is 100 times larger. e. it is 2 times larger.