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?

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:

Where:

- Mass, measured in kilograms.

, - Initial and final speed, measured in meters per second.

- Net external foce, measured in newtons.

- Time, measured in seconds.

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

(2)

If we know that , and , then the time is:

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

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