Suppose you ride a bicycle in a 20-m-radius circle on a horizontal surface. the resultant force exerted by the surface on the bicycle (normal force plus frictional force) makes an angle of with the vertical.
(a) what is your speed?
(b) if the frictional force on the bicycle is half its maximum possible value, what is the coefficient of static friction?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° 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.)

Gas cloud 1 is likely to form a star. gas cloud 2 is not. based on this information, match the given conditions with each cloud

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)