In a Cartesian frame of reference, the potential
energy of an object is
given by u(x) = 6x2 + 2x3
where U is in joules and x
in metres. In addition to
the origin, the position
where the object is in
equilibrium is?

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

In order of decreasing light-transmitting capabilities of materials, which is the correct sequence? a. transparent -> translucent -> opaque b. opaque -> transparent -> translucent c. opaque -> translucent -> transparent d. translucent -> transparent -> opaque

A10 kg box initially at rest is pulled 18 meters across a horizontal, frictionless surface by a 40 n force. what is the block’s final velocity over the 18 meters?