Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 14t i + sin t j + cos 2t k, v(0) = i, r(0) = j

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 ⇒

Aforce of 100 newtons is used to move an object a distance of 15 meters with a power of 50 watts. find the work dine and the time it takes to do the work

Acoil suspended freely, points in some direction when no current is passed through it . can you tell what will happen when a current is passed though it?