Question

Given the kinematics equation for the motion of an object falling from rest, x=.5g*t2), what kind of relationship is predicted between x and t? (select all that apply)

1) x=k*t, where k is a constant

2) x=k*t2, where k is a constant.

3) displacement, x, is proportional to time, t.

4) diplacement, x, is proportional to the square of the time, t2.

5) displacement, x, has a linear relationship with time, t.

6) displacement, x, and time, t, obey a power law.

7) x=k*t+b, where k and b are constants.

Answer 1

Answer on Question#38957 – Physics – Other

Given the kinematics equation for the motion of an object falling from rest, $x = .5g*t2$, what kind of relationship is predicted between $x$ and $t$? (select all that apply)

1) $x = k*t$, where $k$ is a constant

2) $x = k*t2$, where $k$ is a constant.

3) displacement, $x$, is proportional to time, $t$.

4) displacement, $x$, is proportional to the square of the time, $t^2$.

5) displacement, $x$, has a linear relationship with time, $t$.

6) displacement, $x$, and time, $t$, obey a power law.

7) $x = k*t + b$, where $k$ and $b$ are constants.

Solution:

Equations of motion for the object:

$$x = \frac{gt^2}{2} = \frac{g}{2} \cdot t^2 = kt^2$$ $$g = \text{const} = 9.8 \frac{m}{s^2} \Rightarrow$$

First: $x = kt^2$, where $k$ is a constant.

Second: displacement, $x$, is proportional to the square of the time, $t^2$. (Because $x = kt^2 \Rightarrow x \sim t^2$)

Answer: 2) $x = k*t^2$, where $k$ is a constant.

4) displacement, $x$, is proportional to the square of the time, $t^2$.