An ion's position vector is initially r with arrow = 7.0i hat â 7.0j + 1.0k, and 5.0 s later it is r with arrow = 7.0i hat + 7.0j â 8.0k, all in meters. what was its v with arrow avg during the 5.0 s?

Ascientist is tracking an object orbiting the sun that is found between mars and jupiter. in order to classify the object as an asteroid, it must be at least

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Arocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = 12.80 m/s32t, where the +y-direction is upward. (a) what is the height of the rocket above the surface of the earth at t = 10.0 s? b) what is the speed of the rocket when it is 325 m above the surface of the earth?