Consider a block on frictionless ice. Starting from rest, the block travels a distance din time t when force Fis applied. If force 4F is applied, the distance the block travels in
time tis:

The distance is now 4d

Explanation:

Mechanical Force

According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:

F = m.a

Where a is the acceleration of the object.

The acceleration can be calculated by solving for a:

Once we know the acceleration, we can calculate the distance traveled by the block as follows:

If the block starts from rest, vo=0:

Substituting the value of the acceleration:

Simplifying:

When a force F'=4F is applied and assuming the mass is the same, the new acceleration is:

And the distance is now:

Dividing d'/d:

Simplifying:

Thus:

d' = 4d

The distance is now 4d

car a and b are moving in opposite directions

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