A) a block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. the spring projects the block along a frictionless horizontal surface, giving the block a speed v. the same spring projects a second block of mass 4m, giving it a speed 3v. what distance was the spring compressed in the second case?
b) initially a body moves in one direction and has kinetic energy k. then it moves in the opposite direction with three times its initial speed. what is the kinetic energy now?

a)

KE=1/2mv^2

F= -kx

KE= -kx

-kx= 1/2mv^2

when u quadruple the m, the x also quadruples. when the speed is multiplied by 3, since it is v^2, the x is multiplied by 3^2 , which is 9

so distance the spring compressed is x×4×9= 36x

b) using the KE formular too,

when the v is tripled, since formula is v^2, the resulting KE will be multiplied by 3^2, so KE now= 9K

they should be similar or the same

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27