Aparticle moves along a straight line ox. at a time t(in seconds) the distance x(in metres) from the particle o is given by x=40+12t-t3. how long would the particle travel before coming to rest

What is the average speed of a car that travels 40 mph for 1 hour and 60 mph in another hour?

Calculate a pendulums frequency of oscillation (in hz) if the pendulum completes one cycle in 0.5s.

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r