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Exerting any type of force on an object will alter its acceleration. In the case of an object at rest, a force applied to it may not cause it to accelerate immediately, as the applied force may be being countered by the force of friction; in this case, the forces are "balanced" and inertia isn't altered. However, as soon as the applied force is greater than the frictional force, inertia is overcome and the object will accelerate. In the case of the force of gravity, objects revolving around a star, for example, are constantly "falling" towards it due to gravitational attraction, but are also constantly altering their motion and end orbiting around rather than joining with the more massive body.
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