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O-Level Differentiation and integration: worked solution
3 marks. Full working, one step per line.
Question
Given v = 3t² - 8t + 4, find the set of t-values for which this particle travels in a positive sense.
Worked answer
The particle moves in the positive sense when v > 0. 3t² - 8t + 4 > 0 Factorise: (3t - 2)(t - 2) > 0. Critical values t = 2/3 and t = 2. The quadratic (opening upward) is positive outside the roots: t < 2/3 or t > 2. Since t ≥ 0 (time), the particle travels in the positive direction for 0 ≤ t < 2/3 or t > 2.
Practise this topic
This question is part of O-Level Differentiation and integration, in O-Level Additional Maths (A-Maths).
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