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

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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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