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If the velocity of a particle is given by v=√(180-16x)m/s , then its acceleration will be

 

Asked by valavanvino1011 18th July 2018, 11:06 PM
Answered by Expert
Answer:
v equals open parentheses 180 minus 6 x close parentheses to the power of 1 half end exponent
a equals space fraction numerator d v over denominator d t end fraction
fraction numerator d v over denominator d t end fraction equals space 1 half open square brackets open parentheses 180 minus 16 x close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent close square brackets space open parentheses negative 16 fraction numerator d x over denominator d t end fraction close parentheses

W e space k n o w space t h a t space v equals space fraction numerator d x over denominator d t end fraction
rightwards double arrow a equals 1 half open square brackets open parentheses 180 minus 16 x close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent close square brackets space open parentheses negative 16 v close parentheses

S u b s t i t u t e space v a l u e space o f space v space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space

a equals 1 half open square brackets open parentheses 180 minus 16 x close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent close square brackets space open parentheses negative 16 open parentheses 180 minus 6 x close parentheses to the power of 1 half end exponent close parentheses
rightwards double arrow space a space equals 1 half open parentheses 1 over open parentheses 180 minus 16 x close parentheses to the power of begin display style 1 half end style end exponent close parentheses space open parentheses negative 16 open parentheses 180 minus 6 x close parentheses to the power of 1 half end exponent close parentheses

S i m p l i f y i n g space w e space g e t comma
a equals negative 8 space m divided by s squared
thus acceleration is -8m/s2.
Answered by Expert 19th July 2018, 11:16 AM
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