Atire of radius r rolls in a straight line without slipping. its center moves with constant speed v. a small pebble lodged in the tread of the tire touches the road at t = 0. find the pebble’s position, velocity, and acceleration as functions of time.

i've seen solutions before, starting with breaking the motion into x and y coordinates, like so

v(x)=v-rw*cos(wt)

v(y)=v(1-cos(wt))

i do not conceptually understand how these equations are derived, use pictures if nessecary.

Atwo-stage air compressor operates at steady state, compression 10m^3/min of air from 100 kpa and 300k to 1200 kpa. an intercooler between the two stages cools the air to 300k at a constant pressure of 350 kpa. the compression processes are isentropic. a) calculate the power required to run the compressor, in kw b) compare the result to the power required for isentropic compression from the same inlet state to the same final pressure.

How is zig zagging a form of acceleration?

Which of the following correctly describes what happens when an atomic bomb explodes? small pieces of fissionable material are joined and form a body with a mass greater than the critical mass, the relative number of neutrons escaping decreases, and a chain reaction and explosion result. large pieces of fissionable matter are brought together quickly and form a body with a mass smaller than the critical mass, the relative number of escaping neutrons increases, and a chain reaction and explosion result.