Defining the Derivative: Apply It

  • Calculate the slope of a tangent line to a curve and find its equation
  • Find the derivative of a function at a given point
  • Explain how velocity measures speed over time, and compare average velocity over a period with the exact speed at a specific moment

Race to the Finish: Using Derivatives to Analyze Drag Racing Speeds

Two cars are drag racing down a long straight highway. A few bystanders have decided to analyze some pieces of the race, including how fast the cars are traveling and who might win. 

Two cars drag racing

 

The first car’s position, in feet, after t seconds can be described by the function p(t)=25t2. The second car’s position, in feet, after t seconds can be described by the graph.

A graph showing a linear function with a positive slope. The x-axis represents time in seconds, and the y-axis represents the position in feet. The line starts at the origin (0, 0) and increases steadily, indicating constant speed.
Graph of the second car’s position, in feet.