Aplot of potential energy versus position is shown for a 0.16 kg particle that can move along an x-axis as it is acted upon by a conservative force. in the graph, ua = 9 j, uc = 22 j and ud = 29 j (corresponding to x> 8). the particle is released at the point where the potential energy u forms a curved "hill." at this point ub = 13 j and the particle has kinetic energy of 10 j. what is the difference in particle speed when it is located at x= 6.5m compared to x=3.5m, and what is the range of possible particle motion?

Mutt and jeff are running along a path each pushing a cart loaded with rocks. if mutt's wagon has a mass two times greater than jeff's and they want to stay together, arriving at their destination at the same time, what must happen? a) jeff should slow down so mutt can catch up. b) mutt must use half as much force to push his cart. c) mutt must use twice as much force to push his cart. d) mutt and jeff will use the same force, but mutt will take bigger steps.

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

On mars a rock falls an unknown vertical distance from a resting position and lands in a crater. if it takes the rock 2.5 seconds to fall, how high is the cliff the rock fell from? mars' surface gravity is 3.8 m/s2.