A particle $$\(P\)$$ moves in a straight line. It starts at a point $$\(O\)$$ on the line and at time $$\(t\)$$ s after leaving $$\(O\)$$ it has velocity $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$, where $$\(v=4 t^{2}-20 t+21\)$$. Find the minimum velocity of $$\(P\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_43 Year：2020 Question No：5(c)
Answer:
\(8 t-20=0, t=2.5 \rightarrow v=\ldots\) or \(
v=(2 t-5)^{2}-4, v_{\min }=\ldots\)
\[
v_{\min }=-4 \mathrm{~ms}^{-1}
\]
v=(2 t-5)^{2}-4, v_{\min }=\ldots\)
\[
v_{\min }=-4 \mathrm{~ms}^{-1}
\]
Knowledge points:
4.2.3 use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration Calculus required is restricted to techniques from the content for Paper 1: Pure Mathematics 1.
Solution:
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