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The derived units follow the mathematical expressions which relate the quantities. From force equals mass times acceleration, the newton (N) is de ned as the unbalanced force that imparts an acceleration of 1 meter per second squared to a 1-kilogram mass. Thus, 1 N 1 kg m=s2 . Work results when a force acts over a distance. A joule of work is equivalent to a newton-meter: 1 J 1 N m. Work and energy have the same units. Power is the rate at which work is done or the rate at which energy is changed from one form to another. The unit of power, the watt (W), is one joule per second (J/s).

12.54. Find the area of a triangle whose vertices are (a) (0, 0), (2, 3), and (4, 1); (b) (1, 1), (7, 3), and (3, 6); (c) ( 1, 2), (0, 2), and (3, 1). (12.20) 12.55. The vertices of ^ABC are A(2, 1), B(8, 9), and C(5, 7). (a) Find the area of ^ABC. (b) Find the length of AB. (c) Find the length of the altitude to AB. (12.20) 12.56. Find the area of a quadrilateral whose vertices are (a) (3, 3), (10, 4), (8, 7), and (5, 6); (b) (0, 4), (5, 8), (10, 6), and (14, 0); (c) (0, 1), (2, 4), (8, 10), and (12, 2). 12.57. Find the area of the quadrilateral formed by the lines (a) x (b) x (c) x 0, x 0, x 3, x 5, y 7, y 5, y 0, and y 2, and y 3, and y 6 5 8 (d) x (e) y (f) y 0, x 0, y 0, y 6, y 4, y 6, y 0, and y x, and y 2x, and y x x 2x 1 4 6 (12.21) (12.19)

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Table 1-1 Quantity length mass time current Symbol L; l M; m T; t I; i SI Unit meter kilogram second ampere Abbreviation m kg s A

By (6.13),

12.58. Prove each of the following with analytic geometry: (a) A line segment joining the midpoints of two sides of a triangle is parallel to the third side. (b) The diagonals of a rhombus are perpendicular to each other. (c) The median to the base of an isosceles triangle is perpendicular to the base.

Table 1-2 Quantity electric charge electric potential resistance conductance inductance capacitance frequency force energy, work power magnetic ux magnetic ux density Symbol Q; q V; v R G L C f F; f W; w P; p B SI Unit coulomb volt ohm siemens henry farad hertz newton joule watt weber tesla Abbreviation C V

(a) The Q point was established in Problem 3.12 and is indicated in Fig. 3-16. i 3:97 2:0 10 3 0:985 hfb % C iE vCBQ 6:1 V 4 2 10 3 (b) By (6.14), hob % iC 3:05 2:95 10 3 12:5 S vCB IEQ 3 mA 10 2

(d) The length of a line segment joining the midpoints of two sides of a triangle equals one-half the length of the third side. (e) If the midpoints of the sides of a rectangle taken in succession are joined, the quadrilateral formed is a rhombus. (f) In a right triangle, the length of the median to the hypotenuse is one-half the length of the hypotenuse.

EXAMPLE 1.1. In simple rectilinear motion a 10-kg mass is given a constant acceleration of 2.0 m/s2 . (a) Find the acting force F. (b) If the body was at rest at t 0, x 0, nd the position, kinetic energy, and power for t 4 s. a b At t 4 s; F ma 10 kg 2:0 m=s2 20:0 kg m=s2 20:0 N x 1 at2 1 2:0 m=s2 4 s 2 16:0 m 2 2 KE Fx 20:0 N 16:0 m 3200 N m 3:2 kJ P KE=t 3:2 kJ=4 s 0:8 kJ=s 0:8 kW

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