A carbon resistor is 4 mm long and has a constant cross section of 0.2 mm2. The conductivity of carbon at room temperature is 3 × 104 per ohm·m. In a circuit its potential at one end of the resistor is 12 volts relative to ground, and at the other end the potential is 16 volts. Calculate the resistance and the current .

To travel at constant speed, a car engine provides 24kw of useful power. the driving force on the car is 600n. at what speed does it travel?

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 ⇒

Suppose you increase your walking speed from 7 m/s to 13 m/s in a period of 2 s. what is your acceleration?