Advanced mathematics 2 - download pdf or read online

By C. W. Celia, A. T. F. Nice, K. F. Elliott

ISBN-10: 0333231937

ISBN-13: 9780333231937

ISBN-10: 1349035661

ISBN-13: 9781349035663

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Example text

The particle is at the point P, where OP = s, at time t and at the point Q, where OQ = s + bs, at timet + bt. Thus, in moving from P to Q, the particle travels a distance bs in time&. The average velocity of the particle over this interval of time ~tis bs. e. when the particle is at P, is defined as bt l l. e. ck-•0 dt" p Q 0 B ds A Fig. 1 + & is v + ~v, the velocity of the particle has increased by ~v in time&. The average acceleration of If the velocity of the particle at time t is v and at time t the particle over the interval & is ~~.

E. v2 = giving as + c3 where c3 is a constant. e. v = u when s = 0, so C 3 = fv 2 = as + giving v2 = u2 + 2as. e. .. u2 , v2 - u2 = 2as. e. s= (u ; v)t ... (4) Equations (1), (2), (3) and (4) are now used to solve problems concerned with particles and other objects moving with constant acceleration. These equations are used so frequently that they are now collected together for ease of reference.

Use this value as a first approximation to calculate the value of this root correct to three decimal places. [AEB] 51 A solution of the equation x 4 + x 3 + x 2 + x = 5 is known to be x = 1 + h where h is small. 1 approximately. [AEB] 52 The values of x and y given in the table below were obtained in an experiment. It is believed that x and y are connected by a relationship of the form x(y - b) = a, where a and b are constants. Show, by drawing a straight line graph, that this is so. Use your graph to find probable values of a and b.

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Advanced mathematics 2 by C. W. Celia, A. T. F. Nice, K. F. Elliott

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