84
HL Unit 3 (Elite Integration)
Figure 3.10: AB Exam 1997
Problems 3.C-1 (BC Acorn 2000) A particle moves along the x-axis so that at any time t ≥ 0 its velocity is given by v(t) = ln (t + 1) − 2t2 + 4t − 1. (a) What is the total distance traveled by the particle from t = 0 to t = 2? [Ans: 2.178] (b) What is the net displacement of the particle between t = 0 and t = 2? [Ans: 1.963] 3.C-2 (AB ’87) A particle moves along the x-axis so that its acceleration at any time t is given by a(t) = 6t − 18. At time t = 0 the velocity of the particle is v(0) = 24, and at time t = 1 its position is x(1) = 20. (a) Write an expression for the velocity v(t) of the particle at any time t. (b) For what values of t is the particle at rest? (c) Write an expression for the position of the particle at any time t. (d) Find the total distance traveled by the particle from t = 1 to t = 3. Ans: 3t2 − 18t + 24; 2, 4; t3 − 9t2 + 24t + 4; 6 3.C-3 (AB ’93) A particle moves on the x-axis so that its position at any time t ≥ 0 is given by x(t) = 2te−t . Find the total distance traveled by the particle from t = 0 to t = 5. Try this using fnInt, then try this on your calculator, without calculating a definite integral. [Ans: 1.404] Mr. Budd, compiled September 29, 2010