A particle moves along the xxx-axis with velocity v(t)=\ln(t^2+5t+1)v(t)=ln(t 2 +5t+1)v, (, t, ), equals, natural log, (, t, squared, plus, 5, t, plus, 1, ). What is the particle's displacement between the times t=1t=1t, equals, 1 and t=5t=5t, equals, 5?

Two vectors are shown. which statement best compares the vectors? vector x has greater magnitude than vector y. vector y has greater magnitude than vector x. the vectors have the same displacement. the vectors have the same direction.

Find the magnetic field a distance r from the center of a long wire that has radius a and carries a uniform current per unit area j in the positive z direction.

An ice-making machine inside a refrigerator operates in a carnot cycle. it takes heat from liquid water at 0.0 degrees celsius and rejects heat to a room at a temperature of 19.2 degrees celsius. suppose that liquid water with a mass of 76.3kg at 0.0 degrees celsius is converted to ice at the same temperature. take the heat of fusion for water to be l_f = 3.34*10^5 j/kg.how much energy e must be supplied to the device? express your answer in joules.