7) A particle of mass 0.500 kg moves along the x-axiswith a potential energy whose dependence on xis shownbelow. (a) What is the force on the particle atx= 2.00, 5.00, 8.00, and 12.0m? (b) If the totalmechanicalenergy E of the particle is −6.00J, what are the minimumand maximum positions of the particle? (c) What are thesepositions if E = 2.00J? (d) If E = 16.0J , what are thespeeds of the particle at the positions listed in part (a)?

How much heat is needed to change the temperature of 3 grams of gold (c = 0.129 ) from 21°c to 363°c? the answer is expressed to the nearest whole number.

What is magnetic flux? explain faraday's law of induction.

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)