A Weight Is Hung from a Spring and Set in Motion

question 102

Multiple Choice

A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v of the weight at any time t is given by the equation v = 3.5sin 4 πt where v is measured in meters per second and t is measured in seconds. Find the maximum velocity of the weight and the amount of time it takes for the weight to move from its lowest position to its highest position. ​

• A)The maximum velocity is 3.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is seconds.
• B)The maximum velocity is 3.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is seconds.
• C)The maximum velocity is 7 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is seconds..
• D)The maximum velocity is 7 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is seconds.
• E)The maximum velocity is 2.5 meters per second ; the time it takes for the weight to move from its lowest position to its highest position is seconds.

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Definitions:

Total Utility

The overall satisfaction or benefit a consumer receives from consuming a particular quantity of a good or service.

Maximize Utility

The concept in economics that individuals or firms seek to achieve the highest level of satisfaction or benefit from their choices given their resources.

Marginal Costs

The change in total production cost that arises when the quantity produced is incremented by one unit; it is critical for determining the optimal production level.

Theft and Burglary

Crimes involving the unauthorized taking of property; theft is the broader term, while burglary specifically refers to entering a building unlawfully with intent to commit theft or a felony.