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Physics-

General

Easy

Question

A body is at rest at $x equals 0$ . At $t equals 0$ , it starts moving in the positive $x$ -direction with a constant acceleration. At the same instant another body passes through $x equals 0$ moving in the positive $x$ -direction with a constant speed. The position of the first body is given by $x subscript 1 end subscript left parenthesis t right parenthesis$ after time ‘ $t$ ’ and that of the second body by $x subscript 2 end subscript left parenthesis t right parenthesis$ after the same time interval. Which of the following graphs correctly describes $left parenthesis x subscript 1 end subscript minus x subscript 2 end subscript right parenthesis$ as a function of time ‘ $t$ ’

The correct answer is:

$x subscript 1 end subscript equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent$ and $x subscript 2 end subscript equals u t blank therefore x subscript 1 end subscript minus x subscript 2 end subscript equals fraction numerator 1 over denominator 2 end fraction blank a t to the power of 2 end exponent minus u t$
$y equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent minus u t$ .This equation is of parabola
$fraction numerator d y over denominator d t end fraction equals a t minus u$ and $fraction numerator d to the power of 2 end exponent y over denominator d t to the power of 2 end exponent end fraction equals a$
As $fraction numerator d to the power of 2 end exponent y over denominator d t to the power of 2 end exponent end fraction greater than 0 i. e. comma$ graph shows possess minima at $t equals fraction numerator u over denominator a end fraction$

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