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Physics-

General

Easy

Question

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

The correct answer is:

The $v minus x$ equation from the given graph can be written as,
$v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses$
$therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v$
Substituting $v$ from Eq. (i), we get
$a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets$
$blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction$
Thus, $a minus x$ graph is a straight line with positive slope and negative intercept.

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