If you are given values for trianglex, arrow right v, and trianglet, which kinematic equation could be used to find arrow right v o?

Question

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

Answer 1

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:

\[ \Delta x = \vec{v}_0 \Delta t + \frac{1}{2} a (\Delta t)^2 \]