Newtonian model of motion — A/L Combined Mathematics

How do I practise Newtonian model of motion?

1 question with a worked solution

1. A particle moves along a straight line such that its velocity v at position x is given by v² = 16 - 4x. What is the acceleration a of the particle?
   1. A) -2 m s⁻²
   2. B) -8 m s⁻²
   3. C) -4 m s⁻²
   4. D) +4 m s⁻²
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   Correct answer: A) -2 m s⁻²

   Using the kinematic derivative relation for acceleration as a function of position: a = v (dv/dx) = ½ d(v²)/dx. Differentiating v² = 16 - 4x with respect to x gives d(v²)/dx = -4. Therefore, acceleration a = ½ (-4) = -2 m s⁻².

   Show worked solution

   Step 1: Formula: a = ½ · d(v²)/dx. Step 2: d(16 - 4x)/dx = -4. Step 3: a = ½ · (-4) = -2 m s⁻². Answer: -2 m s⁻².
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Newtonian model of motion fit in the syllabus?

Year 2 · Term 2