Answer:
It takes [tex]\frac{1}{2}T[/tex] to accelerate the object from rest to the speed v.
Explanation:
From Newton's second law:
[tex]F=m\cdot a[/tex] (1)
and the definition of acceleration,
[tex]\displaystyle{a = \frac{\Delta v}{\Delta t}}[/tex] (2)
we can solve this problem. Putting (2) in (1) we have:
[tex]\displaystyle{F = m\cdot \frac{\Delta v}{\Delta t}}[/tex] and solving for [tex]\Delta t[/tex] and considering the initial time as zero ([tex]t_0=0[/tex]) and the initial velocity also zero ([tex]v_0=0[/tex]) we have:
[tex]\displaystyle{T=\frac{mv}{F}}[/tex]
Now, for a mass [tex]m^*= 2m[/tex] and the [tex]F^*=4F[/tex] we can wrtie the same equation:
[tex]\displaystyle{T^*=\frac{m^*v}{F^*}}[/tex] and substituting [tex]m^*[/tex] and [tex]F^*[/tex]:
[tex]\displaystyle{T^*=\frac{2m\cdotv}{4F}=\frac{2}{4}T=\boxed{\frac{1}{2}T}}[/tex]
So now, it only takes half the time to accelerate the object from rest to the speed v
