a particle moves along of the x_axis according to the equation X=2t+3t^2, whare x is in m and t is in second. calcualt the instantaneous velocity and the instantaneous acceleration in t=3s​

Agas contained within a piston-cylinder assembly undergoes three processes in series: process 12: compression with pv= constant from 1 bar and 1 liter to 4 bar. process 23: constant pressure expansion to 1 liter. process 31: constant volume calculate the pressure and volume at each state, and sketch the processes on a p-vdiagram labeled with pressure and volume values at each numbered stat

The graph describes the motion of an object. the object moves with from a to b. it from b to c. it moves with from c to d.

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 ⇒