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k is a positive constant and v its speed. At time t = 0, it passes through the origin with speed gT and acceleration g. Show that dv dx gT Hence, obtain an expression for v in terms x,g and T. Prove that at time t, x= gT*in()

k is a positive constant and v its speed. At time t = 0, it passes through the origin with speed gT and acceleration g. Show that dv dx gT Hence, obtain an expression for v in terms x,g and T. Prove that at time t, x= gT*in()

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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(b) A particle P is travelling in the positive direction of the x-axis with acceleration kv?, where k is a positive constant and v its speed. At time t =0, it passes through the origin with speed gT and acceleration g. Show that dv dx gT² Hence, obtain an expression for v in terms x, g and T. Prove that at timet, g7*in) Question 4: (a) (i) State the Principle of Moment (Varignon's Theorem). (ii) Prove that the moment of a couple is the same about any axis perpendicular to the plane of action of the couple. (b) A uniform rod Whose centre of gravity G divides it into the ratio AG : GB = a : b is in limiting equilibrium at an angle a with the horizontal with its upper end B resting against a smooth peg and its lower end A attached to a light cord, which is fastened to a point C on the same level as B. Prove that the angle B at which the cord is inclined to the horizontal is given by the equation a+b tanß = b tana + -cot a a
Transcribed Image Text:(b) A particle P is travelling in the positive direction of the x-axis with acceleration kv?, where k is a positive constant and v its speed. At time t =0, it passes through the origin with speed gT and acceleration g. Show that dv dx gT² Hence, obtain an expression for v in terms x, g and T. Prove that at timet, g7*in) Question 4: (a) (i) State the Principle of Moment (Varignon's Theorem). (ii) Prove that the moment of a couple is the same about any axis perpendicular to the plane of action of the couple. (b) A uniform rod Whose centre of gravity G divides it into the ratio AG : GB = a : b is in limiting equilibrium at an angle a with the horizontal with its upper end B resting against a smooth peg and its lower end A attached to a light cord, which is fastened to a point C on the same level as B. Prove that the angle B at which the cord is inclined to the horizontal is given by the equation a+b tanß = b tana + -cot a a
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