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Yes. If the force applied is smaller than the force of friction for a stationary object or much smaller than the mass x acceleration of a moving object.

You can push a freezer without it moving due to the large frictional force of the heavy object and what it is resting on. If you keep applying a force or you are quite strong you could eventually get it to move.

Similarly, a truck will have no apparent change in motion if it hits a bicycle.

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If a force is applied to an object the object's will change?

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