Starting from position s = 0 m at time t = 0 s, a particle travels on a straight-line path. the particle's velocity is given by the function v = 5 sin (4s2) m/s, where s is in meters and the argument of the sine function is unitless. find the particle's acceleration when s = 0.25 m and s = 1.25 m.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.