Question
If you are given values for trianglex, arrow right v, and trianglet, which kinematic equation could be used to find arrow right v o?
answers:
arrow right v = arrow right v 0 + arrow right a triangle t
triangle x = arrow right v 0^ triangle t + 1/2 arrow right a (triangle t) ^2
triangle x = (arrow right v +arrow right v 0/2) triangle t
arrow v 2 = arrow right v 0 ^2 + 2a triangle x
answers:
arrow right v = arrow right v 0 + arrow right a triangle t
triangle x = arrow right v 0^ triangle t + 1/2 arrow right a (triangle t) ^2
triangle x = (arrow right v +arrow right v 0/2) triangle t
arrow v 2 = arrow right v 0 ^2 + 2a triangle x
Answers
GPT-4o mini
To find \( \vec{v}_0 \) (the initial velocity), you can rearrange any of the kinematic equations that are suitable for the given values.
Among the given equations, the most appropriate is:
**1.** \( \Delta x = \vec{v}_0 \Delta t + \frac{1}{2} a (\Delta t)^2 \)
This equation can be rearranged to solve for \( \vec{v}_0 \):
\[
\vec{v}_0 = \frac{\Delta x - \frac{1}{2} a (\Delta t)^2}{\Delta t}
\]
You would use the known values of \( \Delta x \), \( a \), and \( \Delta t \) to find \( \vec{v}_0 \).
However, if you also have information on other equations, you could use them as well, but this equation directly isolates \( \vec{v}_0 \) conveniently with the given variables.
So, out of the options:
- The most practical choice to find \( \vec{v}_0 \) is:
\[
\Delta x = \vec{v}_0 \Delta t + \frac{1}{2} a (\Delta t)^2
\]
Among the given equations, the most appropriate is:
**1.** \( \Delta x = \vec{v}_0 \Delta t + \frac{1}{2} a (\Delta t)^2 \)
This equation can be rearranged to solve for \( \vec{v}_0 \):
\[
\vec{v}_0 = \frac{\Delta x - \frac{1}{2} a (\Delta t)^2}{\Delta t}
\]
You would use the known values of \( \Delta x \), \( a \), and \( \Delta t \) to find \( \vec{v}_0 \).
However, if you also have information on other equations, you could use them as well, but this equation directly isolates \( \vec{v}_0 \) conveniently with the given variables.
So, out of the options:
- The most practical choice to find \( \vec{v}_0 \) is:
\[
\Delta x = \vec{v}_0 \Delta t + \frac{1}{2} a (\Delta t)^2
\]