Which of these mathematical models would you use to characterize the physical hypothesis below. The hypothesis attempts to predict the y-position of an object undergoing free-fall as a function of time: y = vot + 1/2gt^2
a. Quadratic y = A'x2 + B
b. Inverse Square: y = A/x+B'x
c. Linear y = A"X
d. Quadratic: y = A'X2 + 8'x

D. Quadratic:

Step-by-step explanation:

The kinematic expression is second-order polynomial (quadratic function), whose standard form is:

Where:

, , - Coefficients of the second-order polynomial.

A - Measured in meters per square second.

B - Measured in meters per second.

C - Measured in meters.

- Time, measured in seconds.

- Verticial position, measured in meters.

After a quick comparison, the coefficients are now described:

Where is the gravitational constant, measured in meters per square seconds.

Where is the initial speed, measured in meters per second.

Where is measured in meters.

Hence, the most appropriate hypothesis is using this quadratic form:

The right answer is D.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.