A Particle Moves with Position Function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$

question 71

Multiple Choice

A particle moves with position function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$ .
Find the tangential component of the acceleration vector.

• A) \(a _ { T } = 5 t\)
• B) \(a _ { T } = 542 t\)
• C) \(a _ { T } = 42 t + 5\)
• D) \(a _ { T } = - 55 t\)
• E) \(a _ { T } = 42 t\)

---

Definitions:

Debt Investments

Financial assets representing money lent to an entity (corporate or governmental) that must be paid back with interest.

Historical Cost

The original monetary value of an asset, as recorded on the balance sheet, without adjustments for inflation or market changes.

Brokerage Fees

Charges imposed by a brokerage firm for facilitating transactions, such as buying or selling securities, for its clients.

Loss on Sale

A financial term describing the situation where the selling price of an asset is less than its carrying amount on the balance sheet, resulting in a financial loss.