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The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the velocity of the particle is \( 0.8 m / s \) at \( x=0, \) the velocity of the particle at \( x= \) 1.4 is \( (\text { in } m / s) \)

1. 1.6
2. 1.2
3. \( 1 . \)
4. None of these

Correct answer: 1.6

Solution

For motion along a line with acceleration given as a function of position, use \(a=v\,dv/dx\). Integrating the area under the \(a\)-vs-\(x\) graph from 0 to 1.4 gives the change in \(v^2/2\), which leads to the stated speed.

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