Which of the following depends on an object's displacement not distance from the starting point? a) velocity b) speed c) acceleration d) displacement

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

At very high pressures, gases become and will eventually a) more dense; become hotter b) more dense; change to a liquid or solid c) less dense; combust d) less dense; turn into a liquid