Maths-
General
Easy

Question

A particle moves in a straight line with velocity given by fraction numerator d x over denominator d t end fraction equals x plus 1 (x being the distance described). The time taken by the particle to describe 99 meters is:

  1. log subscript 10 space straight e
  2. 2 log subscript e space 10
  3. 2 log subscript 10 space straight e
  4. 1 half log subscript 10 space e

hintHint:

In this question we have to find t i.e., time taken by the particle to find this we will integrate both sides.

The correct answer is: 2 log subscript e space 10


    fraction numerator d x over denominator d t end fraction equals x plus 1
rightwards double arrow integral subscript 0 superscript 99 fraction numerator d x over denominator x plus 1 end fraction equals integral subscript 0 superscript t d t
rightwards double arrow integral subscript 0 superscript 99 log subscript e open parentheses x plus 1 close parentheses equals t
rightwards double arrow log subscript e open parentheses 100 close parentheses equals t
rightwards double arrow log subscript e open parentheses 10 close parentheses squared equals t
rightwards double arrow 2 log subscript e open parentheses 10 close parentheses equals t

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