Car speed, or velocity, is one example of a derivative, where it is the rate of

Question

Car speed, or velocity, is one example of a derivative, where it is the rate of change in position over a period of time expressed as the following:

This is usually a linear model.

Another function of motion is modeled as a parabola. The following equation represents the height of an object above the ground during a period of time:

h(t) = -16t2 + 112t + 25

where h is the height in feet, and t is time in seconds.

The derivative of this equation will be h' (t) = -32t + 112.

Discuss the following:

Discuss the implication of the time at which the rate of change of the height of the object is equal to 0. What does this point represent?

What other examples can you share where a derivative is applied to real-world applications?

Explanation / Answer

Solution:

Rate of change of height of the object will be zero at imples that speed is zero at this point.

This point represents highest point.

Time taken to reach highest point t = 112 / 32 = 3.5 sec

Real world example.

To find instaneous velocity.

To find maximum and minimum path ( derivative can be used)

In netown's second law.

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