Find the Velocity and Position Vectors of an Object with Acceleration

question 70

Short Answer

Find the velocity and position vectors of an object with acceleration $\mathbf { a } ( t ) = 4 \mathbf { i } - 72 \mathbf { j } + ( 72 t + 4 ) \mathbf { k }$ , initial velocity $\mathbf { v } ( 0 ) = \mathbf { i } + \mathbf { k }$ , and initial position $\mathbf { r } ( 0 ) = \mathbf { j } + 3 \mathbf { k }$ .

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Definitions:

Net Income

This refers to the total profit of a company after all expenses and taxes have been deducted from total revenue.

Variable Cost

Costs that vary in proportion to the volume of goods or services produced, such as materials and labor.

Fixed Costs

Definition: Business expenses that remain the same regardless of the level of production or sales.

Break-Even Point

The moment when the sum of all expenses matches the sum of all income, resulting in neither a profit nor a loss.