Practice problems

A ladybug is crawling in a straight line. At t = 0, her speed is 1 cm/s. She is accelerating at 2 cm/s2. How far has she gone in 3 seconds?

A spool is unwinding. At t = 0, the frequency of rotation is 1 rad/s. The spool is accelerating at 2 rad/s2. What is the change in the angle after 3 seconds?

The angular velocity of a spinning disk is given by w = (18 - 1/2 t2) rad/s. a. At what time does the disk reverse direction? b. Through what angle does the disk turn between t = 0 and the time at which it reverses its direction of rotation? Consider the system below: a bullet is shot through holes in two disks a distance D apart, attached to a shaft that rotates at constant angular speed with a period T. q describes the fixed angular separation of the holes. Derive a formula for the bullet speed v, in terms of given variables.

Check out the animation of this system by Behnam Saeedi.