The force f on an object is the product of the mass m and the acceleration a. in this problem, assume that the mass and acceleration both depend on time t, hence so the does the force. that is, f(t)=m(t)a(t) at time t=7 seconds, the mass of an object is 49 grams and changing at a rate of −1gs. at this same time, the acceleration is 11ms2 and changing at a rate of −10ms3. by the product rule, the force on the object is changing at the rate of .

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.