Aparticle of mass 4.0 kg is constrained to move along the x-axis under a single force f(x) = −cx3 , where c = 8.0 n/m3 . the particle’s speed at a, where xa = 1.0 m, is 6.0 m/s. what is its speed at b, where xb = −2.0 m?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

A100-watt light bulb illuminates a solar cell. the electricity from the solar cell operates a water pump that delivers 1 watt of power. what is the efficiency of the system?

The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. find the period when the length is 144 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 7pi seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.