Question

State the kinematic quantity that is equivalent to the slope of a position-time graph

Answer 1

The slope of a position-time graph represents velocity. For straight sections, it's the average velocity, while the slope of the tangent line on a curve provides the instantaneous velocity.

Step-by-step explanation:

The kinematic quantity that is equivalent to the slope of a position-time graph is velocity. When analyzing a position vs. time graph, the slope can be calculated as the rise over run, which equates to the change in displacement over the change in time. In simpler terms, this means that the slope of the position-time graph represents how quickly the position is changing over time, which is defined as velocity.

For linear sections of the graph, the slope gives the average velocity. If the graph is curved, indicating that the velocity is changing as time progresses, the slope of the tangent line at any given point on the curve will provide the instantaneous velocity at that specific moment.

It is worth noting that if the position-time graph was instead a velocity-time graph, the slope would then represent acceleration, showing how the velocity changes over time.

Answer 2

The figure shows the arrangement of given data.

The displacement is considered along X direction and time along Y direction.

The slope of the graph is given by tan θ

So tan θ = Δx/Δt = Velocity between those two points considered for finding slope of graph.

So slope of position time is graph is equivalent to kinematic quantity Velocity.