Question

From rest, we step on the gas of our Ferrari, providing a force F for 4secs, speed up to a final speed v. If the applied force were only 1/2 F, how long would it have to be applied to reach the same final speed?

Answer 1

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:

$m\cdot (v_{f}-v_{o}) = F \cdot \Delta t$

Where:

$m$ - Mass, measured in kilograms.

$v_{o}$, $v_{f}$ - Initial and final speed, measured in meters per second.

$F$ - Net external foce, measured in newtons.

$\Delta t$ - Time, measured in seconds.

We can eliminate mass and speeds by constructing the following relationship:

$F_{1}\cdot \Delta t_{1} = F_{2}\cdot \Delta t_{2}$ (2)

If we know that $F_{1} = F$, $\Delta t_{1} = 4\,s$ and $F_{2} = \frac{F}{2}$, then the time is:

$4\cdot F = \frac{F\cdot \Delta t_{2}}{2}$

$\Delta t_{2} = 8\,s$

The force must be applied during 8 seconds to reach trhe same final speed.