Answer:
D. instantaneous velocity.
Explanation:
A position-time graph is a graph of the position of an object against (versus) time. The slope of the line of a position-time graph is typically used to determine or calculate the velocity of an object.
In this scenario, Scarlett is analyzing a position-time graph of a moving train. The quantity which can be found by measuring the slope of a line that is tangent to a point on the graph is the instantaneous velocity.
An instantaneous velocity can be defined as the rate of change in position of an object in motion for a short-specified interval of time.
For example.
Given that the equation of motion is S(t) = 10t² + 5t + 20. Find the instantaneous velocity at t = 5 seconds.
Solution.
[tex] S(t) = 5t^{2} + 10t + 20[/tex]
Differentiating the equation, we have;
[tex] S(t) = 10t + 10[/tex]
Substituting the value of "t" into the equation, we have;
[tex] S(t) = 10(5) + 10[/tex]
[tex] S(t) = 50 + 10[/tex]
S(t) = 60m/s.
