To determine whether the statement "The increase of speed is a squared relationship. Three times the speed will have nine times the force of impact" is true or false, let us break down the relationship involved.
1. The statement indicates that the increase of speed is a squared relationship. This means that if you increase the speed by a factor, the impact force will increase by the square of that factor.
2. Let us consider the relationship mathematically. If the original speed is [tex]\(v\)[/tex], and the original force of impact is [tex]\(F\)[/tex]:
- When the speed is increased to [tex]\(3v\)[/tex], the new speed is three times the original speed.
- According to the squared relationship,
- The new force of impact should be proportional to the square of the new speed.
- Thus, the new force of impact [tex]\(F'\)[/tex] is proportional to [tex]\((3v)^2 = 9v^2\)[/tex].
3. Hence, if the original force of impact is [tex]\(F\)[/tex] when the speed is [tex]\(v\)[/tex]:
- The new force of impact [tex]\(F'\)[/tex] when the speed is [tex]\(3v\)[/tex] is [tex]\(9F\)[/tex].
Therefore, three times the speed results in nine times the force of impact, confirming the statement as true.
So the correct answer is:
O a) True
