The acceleration (a) of a particle moving rectilinearly is given by a = 32 - 4y where v is its instantaneous velocity. Also at t=0, x= 0 and v = 4 m/s. (All quantities are measured in SI units). Find v as a function of t: A 4(2-€ 4) B 8(1-25) D 4(2-2-81)

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( a=frac{d v}{d t}=32-4 v ) ( frac{d v}{(32-4 v)}=d t ) ( frac{log _{1}(32-4)}{32-4 v}=e^{-4 t-4 c}=e^{-4(t+2)} ) ( Delta theta quadleft(-infty, v=4, quad 32-16=16=e^{-4(c)}right. ) ( ln 10=-4 c ) ( Rightarrow quad u ln 2=-4 ) ( begin{array}{rl}x & c=-ln 2 32-4 v & =frac{e^{-4 t} times 16}{32-16 e^{-4 t}} 4 v & =3-4 e^{-4 t} v & =4left(2-e^{-4 t}right)end{array} )

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