Answer
$\frac{1}{2}T$
Work Step by Step
- First case:
$m_1=m$, $F_1=F$, $t_1=T$, $v_0=0$ (the object is initially in rest), $v_1=v$
$a_1=\frac{F_1}{m_1}=\frac{F}{m}$
$v_1=v_{0_1}+a_1t_1$.
$v=0+\frac{F}{m}T$
$T=\frac{mv}{F}$
-Second case:
$m_2=2m_1=2m$, $F_2=4F_1=4F$, $v_0=0$ (the object is initially in rest), $v_2=v$
$a_2=\frac{F_2}{m_2}=\frac{4F}{2m}=2\frac{F}{m}$
$v_2=v_{0_2}+a_2t_2$
$v=0+2\frac{F}{m}t_2$
$t_2=\frac{1}{2}\frac{mv}{F}=\frac{1}{2}T$
