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Warm Up

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Warm Up

Read the paragraph at the top of page 267 titled “Chapter 6 Overview”

Then continue to read all of page 267

- Goal: Calculate the distance traveled and use the RAM method.

- Consider an object moving at a constant rate of 3 ft/sec. How far did it go after 4 sec?

Since rate . time = distance:

After 4 seconds, the object has gone 12 feet.

velocity

time

If we draw a graph of the velocity, the distance that the object travels is equal to the area under the line.

If the velocity is not constant,

we might guess that the

distance traveled is still equal

to the area under the curve.

We could estimate the area under the curve by drawing rectangles under the curve.

Area under the velocity curve represents the total distance traveled by an object.

Right-hand Rectangular Approximation

Method .

Left-hand Rectangular Approximation

Method .

Midpoint Rectangular Approximation

Method .

Approximate area:

A particle moves at a velocity of

How far did the particle travel after 4 seconds.

Approximate area:

Same Example using RRAM

1

2

3

4

Example of MRAM

Very similar to the other two.

See example #1 on page 268.

Circumscribed rectangles are all above the curve:

Inscribed rectangles are all below the curve:

- A particle starts at x=0 and travels along the x axis with velocity v(t)=4. Where is the particle at t=7?
- Answer: Find the area of the rectangle under the curve to see the particle is at x=28.