he brake mechanism used to reduce recoil in certain types of gun consists essentially of a piston attached to the barrel and moving in fixed cylinder filled with oil. As the barrel recoils with initial velocity v0, the piston moves and oil is forced through orifices in the piston, causing the piston and the barrel to decelerate at a rate proportional to their velocity; that is, a = -kv. Express a) v in terms of t, b) x in terms of t, c) v in terms of x. Draw the corresponding motion curves.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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The brake mechanism used to reduce recoil in certain
types of gun consists essentially of a piston attached
to the barrel and moving in fixed cylinder filled with oil.
As the barrel recoils with initial velocity v0, the piston
moves and oil is forced through orifices in the piston,
causing the piston and the barrel to decelerate at a
rate proportional to their velocity; that is, a = -kv.
Express a) v in terms of t, b) x in terms of t, c) v in
terms of x. Draw the corresponding motion curves.

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