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A particle of mass \( m \) is moving is a straight line with momentum \( p \). Starting at time \( t=0 \), a force \( F=k t \) acts in the same direction on the moving particle during time interval \( T \) so that its momentum changes from \( p \) to \( 3 p \). Here \( k \) is a constant. The value of \( T \) is [JEE (Main) 2019]
(a) \( \sqrt{\frac{2 k}{p}} \)
(b) \( 2 \sqrt{\frac{k}{p}} \)
(c) \( 2 \sqrt{\frac{p}{k}} \)
(d) \( \sqrt{\frac{2 p}{k}} \)
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