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Calculus, SPEC2 2022 VCAA 14 MC

A particle moving in a straight line with constant acceleration has a velocity of 7 ms\(^{-1}\) at point \(A\) and 17 ms\(^{-1}\) at point \(B\).

The velocity of the particle, in metres per second, at the midpoint of \(AB\) is

  1. \(\sqrt{119}\)
  2. \(11\)
  3. \(12\)
  4. \(13\)
  5. \(\sqrt{240}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Using}\ \ v^2=u^2+2as:\)

\(17^2\) \(=7^2+2as\)  
\(as\) \(=120\)  

 
\(\text{Displacement (halfway)}\ = \dfrac{s}{2} \)

\(v^2\) \(=7^2+2a \times \dfrac{s}{2} \)  
  \(=49+120\)  
  \(=169\)  
\(\therefore v\) \(=13\)  

 
\(\Rightarrow D\)

♦♦♦ Mean mark 28%.