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After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish sonewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

The objection that if the body stops at a certain instant, then the direction of the motion cannot be decided immediately after that instant is untenable. The direction is actually decided by the acceleration, that is by the total force acting on the body at the said instant.

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish somewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

The objection that if the body stops at a certain instant, then the direction of the motion immediately after that instant cannot be decided is untenable. The direction is actually decided by the acceleration, that is by the total force acting on the body at the said instant.

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish sonewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

The objection that if the body stops at a certain instant, then the direction of the motion cannot be decided immediately after that instant is untenable. The direction is actually decided by the acceleration, that is by the total force actiong on the body at the said instant.

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish sonewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

The objection that if the body stops at a certain instant, then the direction of the motion cannot be decided immediately after that instant is untenable. The direction is actually decided by the acceleration, that is by the total force acting on the body at the said instant.

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving on a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish sonewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore the first derivative must be continuous. This derivative is the velocity. You are assuming that it changes its sign passing from time $t$ to time $t'$. A continuous function defined on an interval which changes its sign at the endpoints of the interval must vanish sonewhere in the interval. That is an elementary result of Calculus. In summary, the body must be at rest at some time, if accepting the modern version of Newton's formulation of classical mechanics.

The objection that if the body stops at a certain instant, then the direction of the motion cannot be decided immediately after that instant is untenable. The direction is actually decided by the acceleration, that is by the total force actiong on the body at the said instant.