A0.20 kg particle moves along the x axis under the influence of a stationary object. the potential energy is given by u(x) = 8x2 + 2x4, where u is in joules and x is in meters. if the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

11.18 m/s

Explanation:

Given

mass of particle m=0.2 kg

Potential Energy U(x) is given by

at x=1 m

kinetic energy at x=1 m

Total Energy =U+K.E.

at x=0, U(0)=0

as total Energy is conserved therefore K.E. at x=0 is equal to Total Energy

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.