d, water vapor. gaseous state would have more kinetic energy, they are moving faster. if you have to compare the same state, then higher temperature would have the higher kinetic energy. but if you have solid and liquid at the same temperature - then liquid would have more.
“without loss of generality, we only need to look at the equation for the x-position, since we know that centripetal acceleration points towards the center of the circle. thus, when θ = 0, the second derivative of x with respect to time must be the centripetal acceleration.
the first derivative of x with respect to time t is:
dx/dt = —rsinθ(dθ/dt)
the second derivative of x with respect to time t is:
d2x/dt2 = —rcosθ(dθ/dt)2—rsinθ(d2θ/dt2)
in both of the above equations the chain rule of calculus is used and by assumption θ is a function of time. therefore, θ can be differentiated with respect to time.
now, evaluate the second derivative at θ = 0.
d2x/dt2 = —r(dθ/dt)2
the term dθ/dt is usually called the angular velocity, which is the rate of change of the angle θ. it has units of radians/second.
for convenience we can set w ≡ dθ/dt.
d2x/dt2 = —rw2
this is the well-known form for the centripetal acceleration equation.”
your average speed is:
(the distance you fly, in any convenient unit of length)
the unit of your average speed is:
(the same convenient unit of length) per hour.