Math Problem Statement

The speed, in miles per hour, of a race car on a track is modeled by the linear function v(t) = 60 + 1.2t, where t is the number of seconds since the car began its second lap around the track. Based on the above function, by how many miles per hour is the car's speed increasing for every additional second that passes?

Solution

The function given for the speed of the race car, v(t)=60+1.2tv(t) = 60 + 1.2t, represents the speed v(t)v(t) in miles per hour as a function of time tt, where tt is the number of seconds since the car began its second lap.

In this linear function, the rate of change in speed with respect to time is represented by the coefficient of tt, which is 1.21.2. This means that for every additional second that passes, the car's speed increases by 1.21.2 miles per hour.

Answer:

The car's speed is increasing by 1.2 miles per hour for every additional second that passes.

Would you like more details, or do you have any questions?

Here are five related questions to explore further:

  1. What would the car's speed be after 10 seconds using this function?
  2. How long would it take for the car to reach a speed of 100 miles per hour?
  3. What does the initial value of 60 represent in this context?
  4. If the rate of increase changed to 2 miles per hour per second, what would the new function look like?
  5. How would you determine the time required for the car to double its initial speed?

Tip: In a linear function like this, the coefficient of the variable (here, tt) always represents the rate of change with respect to that variable.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Rate of Change

Formulas

v(t) = 60 + 1.2t

Theorems

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Suitable Grade Level

Grades 8-10