A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by x(t) = [(0.02 m/s3)t3 − (0.41 m/s2)t2 + (1.82 m/s)t − 2.14 m]i. (a) Find an expression for the dancer's velocity as a function of time. (Assume SI units. Do not include units in your answer. Use the following as necessary: t.)

The process in which the nucleus of an atom splits into two lighter atoms, releasing a large amount of energy is nuclear

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?

In order of decreasing light-transmitting capabilities of materials, which is the correct sequence? a. transparent -> translucent -> opaque b. opaque -> transparent -> translucent c. opaque -> translucent -> transparent d. translucent -> transparent -> opaque