Year 12 Maths - Methods (Unit 3 & Unit 4)
Applications of differentiation
Motion in a straight line
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Questions
Question 1
51962
A particle is moving such that its displacement \(x\) cm from the origin after \(t\) seconds is given by:
\[x=t^3-2t^2+t+5\]
Find
i) Formulae for its velocity and acceleration
ii) The initial velocity and acceleration
Part a:
\(v=3t^2-4t+1,\ a=6t-2\)
\(v=3t^2-2t+1,\ a=6t-2\)
\(v=t^2-4t+1,\ a=2t-4\)
\(v=3t^2-4t+1,\ a=6t-4\)
Correct
Part b:
\(v=5\text{ cm/s},\ a=-4\text{ cm/s}^2\)
\(v=1\text{ cm/s},\ a=4\text{ cm/s}^2\)
\(v=1\text{ cm/s},\ a=-4\text{ cm/s}^2\)
Correct
\(v=0\text{ cm/s},\ a=-4\text{ cm/s}^2\)
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