Asmall object is attached to the end of a relaxed, horizontal spring whose opposite end is fixed. the spring rests on a frictionless surface. let the initial position of the object be defined as x-0. the object is pulled to position x = a and then released, after which it undergoes simple harmonic motion. in one full cycle of its motion, the total distance traveled by the object is 2 4 o 4a

Aparticle moves in the xy plane with constant acceleration. at time zero, the particle is at x = 6 m, y = 8.5 m, and has velocity ~vo = (9 m/s) ˆı + (−2.5 m/s) ˆ . the acceleration is given by ~a = (4.5 m/s 2 ) ˆı + (3 m/s 2 ) ˆ . what is the x component of velocity after 3.5 s? answer in units of m/s.

During the apollo moon missions, astronauts were concerned about the effects of newton's third law of motion when: o a. they ejected waste water, because they were concerned that it would push them off course. o b. they reentered earth's atmosphere, because they were carrying heavy moon rocks. o c. they took off from earth, because a large force was required to generate large acceleration. o d. they detected incoming space debris, because the inertia of the debris could damage their ship.

Athird point charge q3 is now positioned halfway between q1 and q2. the net force on q2 now has a magnitude of f2,net = 5.861 n and points away from q1 and q3. what is the value (sign and magnitude) of the charge q3?