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Physics-

General

Easy

Question

A particle moves along $x$ -axis as $x equals 4 open parentheses t minus 2 close parentheses plus a open parentheses t minus 2 close parentheses to the power of 2 end exponent$ Which of the following is true

The initial velocity of the particle is 4
The acceleration of particle is $2 a$
The particle is at origin at $t = 0$
None of these

The correct answer is: The acceleration of particle is $2 a$

$x equals 4 open parentheses t minus 2 close parentheses plus a open parentheses t minus 2 close parentheses to the power of 2 end exponent$
At $t equals 0 comma blank x equals negative 8 plus 4 a equals 4 a minus 8$
$v equals fraction numerator d x over denominator d t end fraction equals 4 plus 2 a left parenthesis t minus 2 right parenthesis$
At $t equals 0 comma blank v equals 4 minus 4 a equals 4 open parentheses 1 minus a close parentheses$
But acceleration, $a equals fraction numerator d to the power of 2 end exponent x over denominator d t to the power of 2 end exponent end fraction equals 2 a$

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