Newtons law of cooling states that if an object with temperature t(t) at time t is in a medium with temperature tm the rate of change of t at time t is proportional to t(t) − tm, thus t satisfies a differential equation of the form t 0 = −k(t − tm) here k > 0, since the temperature of the object must decrease if t > tm, or increase if t < tm. well call k the temperature decay constant of the medium. (a) a thermometer is moved from a room where the temperature is 70f to a freezer where the tem- perature is 12f . after 30 seconds the thermometer reads 40f. what does it read after 2 minutes? (b) an object is placed in a room where the temperature is 20c. the temperature of the object drops by 5c in 4 minutes and by 7c in 8 minutes. what was the temperature of the object when it was initially placed in the room?

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

The electric field direction is defined by the direction of the force felt by (select one of the following answers): 1. a negative charge. 2. a positive charge. 3. both positive and negative charges.

Review multiple-concept example 7 in this chapter as an aid in solving this problem. in a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. in one instance, the radius of the circle is 0.626 m. at one point on this circle, the ball has an angular acceleration of 66.1 rad/s2 and an angular speed of 12.6 rad/s. (a) find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) determine the angle of the total acceleration relative to the radial direction.