Little Triangles & Galileo's Rules
The Little Triangle
A "little triangle" is the region inside the trend line on a velocity graph, that extends from time point 0 units to time point 1 unit. It represents the total displacement from rest during the first unit time interval of motion with constant acceleration.
The displacement from rest during the first unit time interval of motion with constant acceleration is numerically equal to one-half the acceleration.
A "little triangle" is the region inside the trend line on a velocity graph, that extends from time point 0 units to time point 1 unit. It represents the total displacement from rest during the first unit time interval of motion with constant acceleration.
The displacement from rest during the first unit time interval of motion with constant acceleration is numerically equal to one-half the acceleration.
- Δx(0-1) == 1/2 (a)
Galileo's Odd Number Rule
SAGREDO: ... It is thus evident by simple computation that a moving body starting from rest and acquiring velocity at a rate proportional to the time will, during equal intervals of time, traverse distances which are related to each other as the odd numbers beginning with unity, 1,3,5; ...
Galileo Galilei, 1638 (Reference 1)
SAGREDO: ... It is thus evident by simple computation that a moving body starting from rest and acquiring velocity at a rate proportional to the time will, during equal intervals of time, traverse distances which are related to each other as the odd numbers beginning with unity, 1,3,5; ...
Galileo Galilei, 1638 (Reference 1)
Galileo's Duplicate Ratio Rule
SAGREDO: … or considering the total space traversed, that covered in double time will be quadruple that covered during unit time; in triple time, the space is nine times as great as in unit time. And in general the spaces traversed are in the duplicate ratio of the times; i.e., in the ratio of the squares of the times.
Galileo Galilei, 1638 (Reference 1)
SAGREDO: … or considering the total space traversed, that covered in double time will be quadruple that covered during unit time; in triple time, the space is nine times as great as in unit time. And in general the spaces traversed are in the duplicate ratio of the times; i.e., in the ratio of the squares of the times.
Galileo Galilei, 1638 (Reference 1)