If applied force is equal to limiting frictional force, body starts moving.If we continue applying the same force even after the body started in motion,kinetic friction comes into action.When a body is in the state of rest, static frictional force will be zero as it is a self adjusting force.
When we increase the applied force, frictional force also increases and it balances the applied force. Hence body remains in the state of rest. This will happen until the applied force is equal the limiting frictional force.If the applied force is maximum static frictional force, frictional force reach its maximum.It can not increase further and it depends on the nature of the surfaces in contact.
If the applied force is equal to the limiting frictional force,body starts moving. As the body starts moving, frictional force is no more static frictional force and it is kinetic frictional force. We know that when the bodies are in the state of motion, there is no that much scope for interlocking and hence kinetic frictional force is less than static frictional force. For the same reason, coefficient of kinetic friction is less than that of coefficient of static friction.
If we keep applying the same maximum static frictional force even after the body comes into motion on a rough horizontal plane, kinetic friction is less and hence the body starts moving with acceleration. It is just because now there is a resultant force and this gives acceleration to the body.
We can derive the equation for the acceleration as shown below in the video shown.
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