The cart impacts the safety barrier with speed v0 = 3.25 m /s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3 , where x is the amount of spring defl ec- tion from the undeformed position and k1 and k2 are positive constants. if the maximum spring defl ec- tion is 475 mm and the velocity at half-maximum defl ection is 2.85 m /s, determine the values and cor- responding units for the constants k1 and k2.

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.