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.

3. a worker pushes a 30.5 kg polished stone along a polished table with a force on bonin a straight line for 5.20 s after starting from rest. there is no friction between thestone and the table. at the end of the table. the stone is hooked to a cable with a lengthof 62.0 cm to rotate it to a rough table to store until they can be picked up. the roughtable has a coefficient of static friction 0.702 with the polished stone. remember that 8= 9.80 m/s2a) what is the speed of the stone when it is hooked to the cable? b) what is the tension in the cable while the stone is rotating? (there is still nofriction)c) how much force is needed to make the stone begin sliding from rest on therough table? ius = 0.70262.0 cm30.5 kg20.5 kg6= 0