A small object with mass m = 0.0900 kg moves along the +x-axis. The only force on the object is a conservative force that has the potential-energy function U(x)=−αx2+βx3, where α= 7.50 J/m2 and β = 0.300 J/m3. The object is released from rest at small x. When the object is at x = 4.00 m, what are its

(a) speed and
(b) acceleration (magnitude and direction)?
(c) What is the maximum value of x reached by the object during its motion?

Moon effect. some people believe that the moon controls their activities. if the moon moves from being directly on the opposite side of earth from you to being directly overhead, by what percentage does (a) the moon's gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? assume that the earth–moon (center-to-center) distance is 3.82 × 10^8 m, earth's radius is 6.37 × 10^6 m, moon's mass is 7.36 × 10^22 kg, and earth's mass is 5.98 × 10^24 kg.

Arod of some material 0.20 m long elongates 0.20 mm on heating from 21 to 120°c. determine the value of the linear coefficient of thermal expansion [in (degrees c)^-1] for this material.

Ahot-air balloonist, rising vertically with a constant speed of 5.00 m/s releases a sandbag at the instant the balloon is 40.0 m above the ground. after it is released, the sandbag encounters no appreciable air drag. compute the velocity of the sandbag at 0.250 s after its release.