A86.8 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. the astronaut turns away to look at earth and several seconds later is 42.1 m behind the ship, at rest relative to the spaceship. the only way to return to the ship without a thruster is to throw a wrench directly away from the ship. the wrench has a mass of 0.515 kg, and the astronaut throws the wrench with a speed of 19.6 m/s. how long does it take the astronaut to reach the ship

362 seconds, or 6 minutes, 2 seconds.

   This is an exercise in the conservation of momentum. For this problem, I'll use the initial coordinates and velocity of the astronaut as my frame of reference because it makes the math easier. Due to the law of conservation of momentum, the momentum before and after the astronaut throws the wrench has to remain the same. And since I'm using the starting situation of the astronaut as my frame of reference, that value is 0. But thankfully, momentum is a vector quantity and we can save the astronaut.
 The momentum of an object is mass times velocity. So the momentum of the wrench after being thrown is:
  -19.6 m/s * 0.515 kg = -10.094 kg*m/s

   Now to balance that, we need the astronaut to have a momentum of 10.094 kg*m/s which just happens to be the case (can't break the laws of physics). So let's do some division to get the velocity.
 10.094 kg*m/s / 86.8 kg = 0.116290323 m/s

   Yay! The astronaut is moving back to the shuttle at a reasonable velocity. But has 42.1 m to travel. Another situation for division: 42.1 m / 0.116290323 m/s = 362.0249653 s

    So rounding to 3 significant digits gives a travel time of 362 seconds, or just a couple of seconds longer than 6 minutes.

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Well the magnitude of its acceleration related to that car starts with the oil change like when you have to change the oil in your car you have to make sure that your precious car is starting really propley and very well