Answer:
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:
[tex]\displaystyle a=\frac{F}{m}[/tex]
Once we know the acceleration, we can calculate the distance traveled by the block as follows:
[tex]\displaystyle d = vo.t+\frac{at^2}{2}[/tex]
If the block starts from rest, vo=0:
[tex]\displaystyle d = \frac{at^2}{2}[/tex]
Substituting the value of the acceleration:
[tex]\displaystyle d = \frac{\frac{F}{m}t^2}{2}[/tex]
Simplifying:
[tex]\displaystyle d = \frac{Ft^2}{2m}[/tex]
When a force F'=4F is applied and assuming the mass is the same, the new acceleration is:
[tex]\displaystyle a'=\frac{4F}{m}[/tex]
And the distance is now:
[tex]\displaystyle d' = \frac{4Ft^2}{2m}[/tex]
Dividing d'/d:
[tex]\displaystyle \frac{d' }{d}=\frac{\frac{4Ft^2}{2m}}{\frac{Ft^2}{2m}}[/tex]
Simplifying:
[tex]\displaystyle \frac{d' }{d}=4[/tex]
Thus:
d' = 4d
The distance is now 4d
