- #1

sma14

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v=1(3t+2) (m/s) for 0 ≤t ≤8, n=4

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In summary, the problem involves approximating the displacement of an object on a specific interval using the left endpoint of each subinterval to compute the height of rectangles. The function v= 1(3t+2) (m/s) is given for 0 ≤t ≤8 and n=4 subintervals. The heights of the rectangles are calculated at t= 0, 2, 4, and 6 and the total area is determined by adding the areas of the four rectangles.

- #1

sma14

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v=1(3t+2) (m/s) for 0 ≤t ≤8, n=4

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- #2

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What have you been able to do so far? This is most easily discussed as a graphing problem.sma14 said:

v=1(3t+2) (m/s) for 0 ≤t ≤8, n=4

-Dan

- #3

HOI

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In any case, you are told exactly what to do in the problem:

Approximate the displacement of the object on the interval by subdiving the interval into the indicated number of subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles

v=1(3t+2) (m/s) for 0 ≤t ≤8, n=4

Dividing 0 to 8 into 4 subintervals means [0, 2], [2, 4], [4, 6], and [6, 8]. Although the height of the function varies continuously, you are told to "use the left endpoint of each subinterval to compte the height". So you are approximating the area under the curve by 4 rectangles, each with length 2 and heights calculated at t= 0, 2, 4, and 6.

If v really is 1(3t+ 2) then those heights are 1(3(0)+ 2)= 2, 1(3(2)+ 2)= 8, 1(3(4)+ 2)= 14, and 1(3(6)+ 2)= 20. What are the areas of those four rectangles? What is the total area. But if v= 1/(t+ 2), the heights are 1/(0+ 2), 1/(2+ 2), 1/(4+ 2), and 1/(6+ 2). What are the areas of those rectangles? What is the total area?

Velocity is a measure of an object's displacement over time. It is a vector quantity, meaning it has both magnitude (speed) and direction. Speed, on the other hand, is a scalar quantity that only measures the rate of change of an object's position without regard to direction.

Velocity can be calculated by dividing the displacement of an object by the time it took to travel that distance. The formula for velocity is v = Δx/Δt, where v is velocity, Δx is the displacement, and Δt is the time interval.

The standard units for velocity are meters per second (m/s) in the metric system and feet per second (ft/s) in the imperial system. However, other units such as kilometers per hour (km/h) or miles per hour (mph) may also be used.

Yes, velocity can be negative. This indicates that the object is moving in the opposite direction of its positive velocity. For example, if an object has a velocity of -5 m/s, it is moving 5 meters per second in the negative direction.

Velocity is an important concept in physics and is used to solve various problems related to motion. It can be used to calculate an object's acceleration, displacement, and time of travel. It is also used in the study of forces, energy, and other fundamental principles of physics.

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