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Using the Difference Quotient to Calculate Average Velocity

A ball is released at the top of a ramp (an inclined plane). The distance it travels can be expressed as the function:

s(t)=5t^2, where t is the time in seconds after the ball is released.

The distance function, s(t), is measured in feet. Find the average velocity of the ball for the time interval [1,4].

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Solution Preview

This is a difference quotient problem. The standard form of the difference quotient is:

( f(x + h) - f(x) ) / h, h not equal to 0.

(Please note the parentheses - the entire numerator is f(x+h) - f(x). Both terms are over h.)

When working with ...

Solution Summary

The difference quotient is important to understand for those studying college algebra and trigonometry and for those preparing for calculus. Calculating average velocities is a practical and readily understood application of the difference quotient. In this problem, we rewrite the difference quotient using the given distance function and apply it to find the average velocity, during a specified time interval, of a ball rolling down an incline plane. The solution includes a step-by-step explanation and provides a review of evaluating a function at a given value.