Question

Scarlett is analyzing a position-time graph of a moving train. Which quantity can be found by measuring the slope of a line that is tangent to a point

on the graph?

acceleration
displacement
average velocity
instantaneous velocity

Answer 1

D. instantaneous velocity.

Step-by-step 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.

`S(t) = 5t^(2) + 10t + 20`

Differentiating the equation, we have;

`S(t) = 10t + 10`

Substituting the value of "t" into the equation, we have;

`S(t) = 10(5) + 10`

`S(t) = 50 + 10`

S(t) = 60m/s.