On its own, a certain tow-truck has a maximum acceleration of 3.0 m/s2. what would be the maximum acceleration when this truck was towing a bus of twice its own mass?

Let's call  the maximum acceleration of the truck alone. The force produced by the engine to accelerate the truck in this situation is

with m being the mass of the truck alone.

If we attach a bus of twice the mass of the truck, now the whole system (truck+bus) has a mass of (m+2m)=3m. And in this case, the force produced by the engine is

with a2 being the new acceleration. 
The engine is always the same, so the force produced is still the same, so we can equalize F written in the first equation and in the second equation:

and find a2, the new acceleration:

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.