Using approximate values, calculate the slope of the curve...

Using approximate values, calculate the slope of the curve in Figure 2.74 to verify that the velocity at $t=30.0 \mathrm{s}$ is 0.238 $\mathrm{m} / \mathrm{s}$ . Assume all values are known to 3 significant figures.

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Key Concepts

Derivative

The derivative of a function at a given point represents the instantaneous slope or rate of change of the function at that point. In the context of physical motion, it is used to determine variables like velocity, which is the derivative of displacement with respect to time.

Finite Difference Approximation

Finite difference methods provide a way to approximate the derivative of a function when only discrete data points are available. By calculating the ratio of differences in function values to differences in the independent variable, one can estimate the instantaneous rate of change.

Velocity as a Derivative

In physics, velocity is defined as the derivative of the displacement (or position) function with respect to time. This means that by determining the slope of the displacement-time curve at a specific moment, one can obtain the instantaneous velocity at that moment.

Significant Figures

Significant figures are used to reflect the precision of measured or calculated values. When performing calculations with approximate values, it is important to round the intermediate and final results according to the prescribed level of precision to maintain the reliability of the computed quantities.

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