Question

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

Answer 1

Answer:

D. Quadratic: $y = A\cdot x^{2}+B\cdot x$

Step-by-step explanation:

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

$y = A\cdot t^{2} + B\cdot t + C$

Where:

$A$, $B$, $C$ - Coefficients of the second-order polynomial.

A - Measured in meters per square second.

B - Measured in meters per second.

C - Measured in meters.

$t$ - Time, measured in seconds.

$y$ - Verticial position, measured in meters.

After a quick comparison, the coefficients are now described:

$A = \frac{1}{2}\cdot g$

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

$B = v_{o}$

Where $v_{o}$ is the initial speed, measured in meters per second.

$C = 0$

Where $C$ is measured in meters.

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

$y = A\cdot x^{2}+B\cdot x$

The right answer is D.