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Maths-

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Question

The equation of motion of a particle moving along a straight line is s=2 $t to the power of 3 end exponent minus 9 t to the power of 2 end exponent plus 12 t comma$ where the units of s and t are centimeter and second. The acceleration of the particle will be zero after

$\frac{3}{2} s$
$\frac{2}{3} s$
$\frac{1}{2} s$
1s

The correct answer is: $fraction numerator 3 over denominator 2 end fraction s$

Given $blank s equals 2 t to the power of 3 end exponent minus 9 t to the power of 2 end exponent plus 12 t rightwards double arrow fraction numerator d s over denominator d t end fraction equals 6 t to the power of 2 end exponent minus 18 t plus 12 blank$
Again , $fraction numerator d to the power of 2 end exponent s over denominator d t to the power of 2 end exponent end fraction equals 12 t minus 18 equals a c c e l e r a t i o n$

If acceleration becomes zero, then

$0 equals 12 t minus 18 rightwards double arrow t equals fraction numerator 3 over denominator 2 end fraction s$

Hence, acceleration will be zero after = $fraction numerator 3 over denominator 2 end fraction s.$

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