An 8 kg block is pushed across a horizontal surface by a horizontally oriented force whose magnitude varies in time. The instantaneous power supplied by the pushing force to the block is P subscript p u s h end subscript open parentheses t close parentheses equals open parentheses 4 straight W over straight s cubed close parentheses t cubed If the block starts at rest at t = 0 s, what is the displacement (in m) of the block after 3 s?

Suppose you were asked to find the torque about point p due to the normal force n in terms of given quantities. which method of finding the torque would be the easiest to use?

Unpolarized light falls on two polarizer sheets whose transmission axes are at right angles. a third polarizer is placed between the first two so that its axis makes a 52-degree angle with the axis of the first polarizer. a) what fraction of the incident light intensity is transmitted through the first polaroid? b) what fraction of the incident light intensity is transmitted through the second polaroid? c) what is the angle of polarization of the light that enters the third polaroid? d) what fraction of the incident light intensity is transmitted through the third polaroid. e) what happens if the middle polaroid is removed?

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)