The Position of a Particle Is Given by the Function $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$

question 106

Essay

The position of a particle is given by the function s(t) = $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$ , where t is measured in seconds and s in meters.(a) Find the velocity at time t.(b) When is the particle at rest?
(c) When is the particle moving in the positive direction?
(d) Draw a diagram to represent the motion of the particle.(e) Find the total distance traveled by the particle during the time interval [1,3].

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Interest Rate

The percentage at which interest is paid by a borrower for the use of money they borrow from a lender.

Present Value

The current worth of a future sum of money or stream of cash flows given a specified rate of return.

Endowment

In economics, an endowment is the total range of assets, including both physical goods and intangible elements like labor skills, that an individual or entity owns.

Interest Rate

The proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage of the loan amount.