The position vector for a particle moving on a helix is c(t)= (cost, sint, t^2). find the speed of the particle at time t = 4pi

Apulley with mass mp and a radius rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot.

Question part points submissions used suppose that 2 j of work is needed to stretch a spring from its natural length of 26 cm to a length of 36 cm. (a) how much work is needed to stretch the spring from 28 cm to 32 cm? (round your answer to two decimal places.)

Aplayground merry-go-round has a radius of 4.6 m and a moment of inertia of 200 kg-m2 and turns with negligible friction about a vertical axle through its center. a child applies a 26.0 n force tangentially to the edge of the merry-go-round for 15.0 seconds. if the merry-go-round is initially at rest, how much work did the child do on the merry-go-round?