UNIVERSITY OF JOHANNESBURG SEMESTER TEST 1 21 August 2014 Time: 60min Marks: 25 APM 1B Calculators are permitted. Angles are in radians. All physical quantities are in SI units. QUESTION 1 [13] The position vector of a particle is t3 x b + (sin t) yb r (t) = Determine, for t = 1; t3 ; sin t : (a) r; v and a. (b) r; v and a: (c) rb and b: (d) r_ and r•: (e) _ ; • and : QUESTION 2 [12] Given the following a (t) = cos t; 6t; et + 2 r (0) = (0; 0; 0) r (1) = (3; 2; 1) ; determine v (0) : ____________________________________________ v = a = dr = r_ dt dv = v_ dt v = vr rb + v b = rb _r + r _ b rb = (cos ; sin ) a = r• r_ 2 v = jvj rb + r• + 2r_ _ b b = ( sin ; cos ) r= Z vdt + C
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