Question # The position of a particle moving along x-axis given by ( x=left(-2 t^{3}+3 t^{2}+5right) m . ) The acceleration of particle at the instant its velocity becomes zero is

# The position of a particle moving along x-axis given by ( x=left(-2 t^{3}+3 t^{2}+5right) m . ) The acceleration of particle at the instant its velocity becomes zero is

(1) ( 12 mathrm{m} / mathrm{s}^{2} )

(2) ( -12 mathrm{m} / mathrm{s}^{2} )

(3) ( -6 mathrm{m} / mathrm{s}^{2} )

(4) Zero

Solution

( quad x=-2 t^{3}+3 t^{2}+5 )

( begin{aligned} v=& frac{d x}{d t}=-6 t^{2}+6 t+0 &=-6 t^{2}+6 t=6 t(1-t) end{aligned} )

( v=0 quad ) at ( t=0 ) and ( t=1 )

( frac{d v}{d t}=frac{d}{d t}left(-6 t^{2}+6 tright) )

( =-12 t+6 )

( t=180, quad a=-12+6=-6 mathrm{m} / mathrm{s}^{2} )

Option (3)