smc-7437-80-Graph

The graph shows the velocity of a particle as a function of its displacement.

Which of the following graphs best shows the acceleration of the particle as a function of its displacement?

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\(A\)

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\(\text{By elimination:}\)

\(v(x)\ \Rightarrow\ \text{degree 3 (see graph)},\ \ \dfrac{dv}{dx}\ \Rightarrow\ \text{degree 2}\)

\(a=v \cdot \dfrac{dv}{dx}\ \Rightarrow\ \text{degree 5 (eliminate C and D)}\)

\(\text{At}\ \ x=0,\ \ v(x)>0\ \ \text{and}\ \ \dfrac{dv}{dx}<0\ \ \Rightarrow\ \ v \cdot \dfrac{dv}{dx} \neq 0\ \text{(eliminate B)}\)

\(\Rightarrow A\)

♦♦ Mean mark 35%.