Question
What is the direction of instantaneous velocity of a body at a specific instant?
Answers
GPT-4o mini
The instantaneous velocity of a body at a specific instant is defined as the rate of change of its position with respect to time at that moment. In terms of direction, the instantaneous velocity vector points in the direction of the object's motion at that particular instant.
Mathematically, it can be expressed as:
\[
\vec{v} = \frac{d\vec{x}}{dt}
\]
where \(\vec{v}\) is the instantaneous velocity, \(\vec{x}\) is the position vector, and \(t\) is time.
To summarize, the direction of instantaneous velocity is the same as the direction of motion of the object at that instant. If the object is moving in a straight line, the instantaneous velocity will point in the same direction as that line. If the object is changing direction, the instantaneous velocity will point along the tangent to the path of motion at that specific moment.
Mathematically, it can be expressed as:
\[
\vec{v} = \frac{d\vec{x}}{dt}
\]
where \(\vec{v}\) is the instantaneous velocity, \(\vec{x}\) is the position vector, and \(t\) is time.
To summarize, the direction of instantaneous velocity is the same as the direction of motion of the object at that instant. If the object is moving in a straight line, the instantaneous velocity will point in the same direction as that line. If the object is changing direction, the instantaneous velocity will point along the tangent to the path of motion at that specific moment.