# How to calculate time needed by an object to change its state of motion when an net force applies to it (inertia)?

(Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to "resist" changes in a state of motion is inertia.) How to calculate the time an motionless object will "resist" to changes when an net force applied?

• The acceleration is the applied force divided by the mass of the object. There is no ‘delay’. Feb 16 at 18:51

Newton's second law of motion says that the net force on an object is equal to the object's acceleration multiplied by its mass. So, if a net force $$\vec F$$ is applied to an object with mass $$m$$, its acceleration is

$$\displaystyle \vec a = \frac {\vec F} m$$

If a net force $$\vec F$$ is applied to an object that is initially at rest then the object begins to move immediately. If the force $$\vec F$$ is applied for a time $$t$$ then at the end of the time $$t$$ the object's velocity $$\vec v$$ is

$$\displaystyle \vec v = \vec a t = \frac {\vec F t} m$$

As noted in @gandalf61's answer, for an ideal point mass subject to a single force with no friction or other resistive forces, the object starts moving the instant the force is applied. There is no delay.

For a real macroscopic object, the side of the object where the force is applied will start to move instantaneously, but it takes time for the force to propagate throughout the object. The force propagates at the speed of sound ($$v$$) in the object's material, so for an object of size $$L$$, it takes a time $$t\sim L/v$$ for every part of the object to start moving.

Theoretically, the time is zero as the effects of a force are felt instantaneously. As soon as the force is applied, the center of mass of the object is going to start squirting some velocity and the body will proportionately have momentum.

In practice, each object is neither a point mass, nor a rigid body, and thus as soon as a force is applied at some location, local deformation occurs. At this instant deformation waves, or stress waves start to travel throughout the body at the speed of sound inside the body.

As a result, the effect of the force is felt by each part of the body at different times. And this situation is measurable with simple experiments.

Resistance to changes should not interpreted as if, at some time, there is a sudden drop in the ability to resist. Instead, it means that the larger the mass, the smaller the resulting acceleration in the presence of the same force.