Theory question 115
Vectors(a) Given that m = i − j, n = 2i + 3j and 2m + n − r = 0, find |r|. (b) The distance, S metres of a moving particle at any time t seconds is given by S = 3t − t3/3 + 9. Find the: (i) time; (ii) distance travelled; when the particle is momentarily at rest.
Show the model answer
Model answer
(a) r = 2m + n = 4i + j; |r| = √17 ≈ 4.12.
(b)(i) v = 3 − t² = 0 at t = √3 ≈ 1.73 s.
(ii) S(√3) = 3√3 − √3 + 9 = 9 + 2√3 ≈ 12.46 m; since S = 9 at t = 0, the particle has travelled 2√3 ≈ 3.46 m by then.
Explanation
Momentarily at rest means v = dS/dt = 0.