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Maths-

General

Easy

Question

If A,B,C are the maximum velocities of the particles moving according to the law $S equals 60 t minus 5 t to the power of 3 end exponent comma S equals 6 t minus fraction numerator 1 over denominator 2 end fraction t to the power of 3 end exponent comma S equals 10 t minus 7 t to the power of 3 end exponent$ respectively then the ascending order of A,B,C is

A, B, C
C, B, A
$B, A, C$
B,C,A

hint Hint:

The quantity ds/dt is called the derivative of s with respect to t, or the rate of change of s with respect to t. It is possible to think of ds and dt as numbers whose ratio ds/dt is equal to v; ds is called the differential of s, and dt the differential of t.

The correct answer is: B,C,A

Complete step by step solution
Given :
$S subscript A equals 60 t minus 5 t cubed comma S subscript B equals 6 t minus 1 half t cubed comma S subscript C equals 10 t minus 7 t V subscript A space equals space fraction numerator d s subscript A over denominator d t end fraction equals space 60 space minus space 5 space left parenthesis space 3 t squared right parenthesis space equals space 60 space minus space 15 t squared space......... space left parenthesis 1 right parenthesis end subscript V subscript B space equals space fraction numerator d s subscript B over denominator d t end fraction equals space 6 space minus space 1 half space left parenthesis space 3 t squared right parenthesis space equals space 6 space minus space 3 over 2 t squared space......... space left parenthesis 2 right parenthesis end subscript V subscript C space equals space fraction numerator d s subscript C over denominator d t end fraction equals space 10 space minus space 7 space left parenthesis space 3 t squared right parenthesis space equals space 10 space minus space 21 t squared space......... space left parenthesis 3 right parenthesis end subscript F o r comma space V subscript m i n end subscript comma space fraction numerator d v over denominator d t end fraction space i s space m a x space a t space t space equals space 0 S u b s t i t u t i n g space t h e space v a l u e space o f space t space equals space 0 space i n space 1 comma 2 comma 3 comma space w e space g e t V subscript A space equals space 60 space end subscript V subscript B space equals space 6 space end subscript V subscript C space equals space 10 space end subscript A r r a n g i n g space i s space a s c e n d i n g space o r d e r B space less than space C space less than space A space$

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