Answer:
The force must be applied during 8 seconds to reach trhe same final speed.
Explanation:
By Impulse Theorem, a change in the magnitude of linear momentum of a system with constant mass can be done by applying a force during a given time. That is:
[tex]m\cdot (v_{f}-v_{o}) = F \cdot \Delta t[/tex]
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v_{o}[/tex], [tex]v_{f}[/tex] - Initial and final speed, measured in meters per second.
[tex]F[/tex] - Net external foce, measured in newtons.
[tex]\Delta t[/tex] - Time, measured in seconds.
We can eliminate mass and speeds by constructing the following relationship:
[tex]F_{1}\cdot \Delta t_{1} = F_{2}\cdot \Delta t_{2}[/tex] (2)
If we know that [tex]F_{1} = F[/tex], [tex]\Delta t_{1} = 4\,s[/tex] and [tex]F_{2} = \frac{F}{2}[/tex], then the time is:
[tex]4\cdot F = \frac{F\cdot \Delta t_{2}}{2}[/tex]
[tex]\Delta t_{2} = 8\,s[/tex]
The force must be applied during 8 seconds to reach trhe same final speed.
