Lesson: Instantaneous Speed Physics • 9th Grade

In this lesson, we will learn how to determine the instantaneous speed of an object by using a tangent to find the slope at a point on the object's displacement–time graph.

Lesson Plan

Students will be able to

  • identify from straight-line displacement–time graphs what the speed of an object at a particular instant in time is (as opposed to over a time range),
  • correctly identify tangents to curves on displacement–time graphs,
  • use tangents to curves to find the speed of an object at an instant,
  • recognize that if the tangent is a horizontal line, then the speed is zero,
  • recognize that the greater the slope of the tangent, the greater the instantaneous speed at that point.

Lesson Video

Video Thumbnail
12:21

Lesson Explainer

Sample Question Videos

  • 01:51
  • 03:30
  • 02:23

Lesson Worksheet

Q1:

An object moves along a straight line. On the graph, the blue line shows the displacement, 𝑑, of the object from its starting position over time, 𝑡.

Which of the three dashed lines is a tangent to the blue line at 𝑡=4 s?

Which of the three dashed lines is a tangent to the blue line at 𝑡=1 s?

Which of the three dashed lines is a tangent to the blue line at 𝑡=16 s?

Q2:

An object moves along a straight line. On the graph, the blue line shows the displacement, 𝑑, of the object from its starting position over time, 𝑡.

Which of the three dashed lines is a tangent to the blue line at 𝑡=4 s?

Q3:

A ball is thrown up in the air, and it falls back down to the ground. The height, ℎ, of the ball above the ground over time, 𝑡, is shown on the graph by the blue line. The red line is a tangent to the blue line at 𝑡=1 s. What is the speed of the ball at 𝑡=1 s?

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