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differentiate between drag force and terminal speed. derive escape velocity.

Dear Student ,
Drag force is the resistance force which is caused by the motion of a body through a liquid or air .drag force acts on the opposite direction of motion of a body in a fluid .
Now the terminal velocity is the highest attainable velocity of a body when the body falls freely through a fluid .The terminal velocity occurs when the sum of the drag force and buoyancy force is equal to the down ward gravity force due to the weight of the body .

Here is a link which will help you to derive the expression for escape velocity .
https://www.meritnation.com/ask-answer/question/derivation-of-escape-velocity/physics/4126375

Regards

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Drag Force A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is the relative velocity between the body and the fluid. 

Terminal velocity is the highest velocity attainable by an object as it falls through a fluid (air is the most common example, but the concept applies equally to any fluid). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object.

Escape velocity 
the lowest velocity which a body must have in order to escape the gravitational attraction of a particular planet or other object.
 
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