A marble slides along a frictionless track at a constant speed u before encountering a section of the track that is covered with a thin layer of putty. The instantaneous velocity v of the marble as it slides past the putty, as a function of time t, is given byv(t)=u-bt+ct^3where t = 0 at the moment when the marble first comes into contact with the putty. As the marble exits the region covered in putty, the marble\'s instantaneous acceleration goes to zero. For u = 2.50 m/s, b = 3.55 m/s2, and c = 6.70 m/s4, calculate the length of the track that is covered with putty. m

In what direction does an applied force move an object? in the same direction as the force independent of the force in the opposite direction of the force perpendicular to the force

Air enters a compressor operating at steady state at 1.05 bar, 300 k, with a volumetric flow rate of 93 m3/min and exits at 12 bar, 400 k. heat transfer occurs at a rate of 15.5 kw from the compressor to its surroundings. assuming the ideal gas model for air neglecting kinetic potential energy effects, determine the power in put in kw.

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)