Suppose a Particle Is Moving in the Xy-Plane So That $\mathbf { r } ( t ) = \left\langle t ^ { 3 } - t , t - t ^ { 2 } \right\rangle$

question 94

Essay

Suppose a particle is moving in the xy-plane so that its position vector at time t is given by $\mathbf { r } ( t ) = \left\langle t ^ { 3 } - t , t - t ^ { 2 } \right\rangle$ . Find the velocity, speed, and acceleration of the particle at time t = 2.

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Definitions:

Marginal Costs

The cost associated with producing one additional unit of a product or service.

Variable Costs

Expenses that change in proportion to the activity or volume of operations in a business.

Fixed Costs

Fixed charges that are unaffected by changes in production volume, including rental fees and payrolls.

Variable Cost Curve

The variable cost curve shows the relationship between total variable cost and the level of a firm's output, demonstrating how costs fluctuate with changes in production.