40.0 11. The electric resistance R (in ) of a certain resistor as a function of

Question

40.0 11. The electric resistance R (in ) of a certain resistor as a function of the temperature T (in °C) is R 4.000 + 0.00378. If the tem- perature is increasing at the rate of 0.100°C/s, find how fast the resistance changes when T = 150°C. 12. The kinetic energy K (in J) of an object is given by K = where m is the mass (in kg) of the object and v is its velocity. If a 250-kg wrecking ball accelerates at 5.00 m/s2, how fast is the kinetic energy changing when u = 30.0 m/s? 13. The length L (in in.) of a pendulum is slowly decreasing at the rate of 0.100 in./s. What is the time rate of change of the period T (in s) of the pendulum when L 16.0 in, if the equation relating the period and length is T = VL/96? 14. The voltage V that produces a current I (in A) in a wire of radius r (in in.) is V = 0.0301/r2. If the current increases at 0.020 A/s in a wire of 0.040 in. radius, find the rate at which the voltage is increasing. 15. A plane flying at an altitude of 2.0 mi is at a direct distance D = V4.0+r from an airport control tower, where x is the horizontal distance to the tower. If the plane's speed is 350 mi/h, how fast is D changing when x = 6.2 mi? See Fig. 24.24. 2.0 mi Fig. 24.24

Explanation / Answer

V=0.030I/r2

Differentiting both sides

dV/dt=(0.030/r2)(dI/dt)

dV/dt=(0.030/(0.040)2) * 0.020 = 0.375

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