Question

1. which of the following is the correct mathematical definition for velocity?

$overrightarrow{v}=\frac{\delta t}{\overrightarrow{d}}$
$overrightarrow{v}=\frac{\overrightarrow{d}}{\delta t}$
$v = \frac{d}{\delta t}$
$v = \frac{\overrightarrow{d}}{\delta t}$

Explanation:

Velocity is a vector quantity. It is defined as the displacement (a vector, denoted as \(\vec{d}\)) divided by the time interval (\(\Delta t\)). The formula for velocity (\(\vec{v}\)) is \(\vec{v}=\frac{\vec{d}}{\Delta t}\). The first option has the formula inverted. The third option \(v = \frac{d}{\Delta t}\) gives speed (a scalar quantity) as it uses distance (\(d\), a scalar) instead of displacement (\(\vec{d}\), a vector). The fourth option \(v=\frac{\vec{d}}{\Delta t}\) uses \(v\) (which is typically for scalar speed) with a vector displacement, which is inconsistent notationally.

Answer:

\(\vec{v}=\frac{\vec{d}}{\Delta t}\) (the second option)