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A force $\vec{F} = 6t^2\,\hat{i} + 4t\,\hat{j}$ acts on a particle of mass $3\text{ kg}$, initially at rest. Find its velocity at $t = 3\text{ s}$.
Acceleration: $\vec{a} = \dfrac{\vec{F}}{m} = 2t^2\,\hat{i} + \dfrac{4t}{3}\,\hat{j}$
Velocity: $\vec{v} = \displaystyle\int_0^3 \vec{a}\,dt = \left[\dfrac{2t^3}{3}\,\hat{i} + \dfrac{2t^2}{3}\,\hat{j}\right]_0^3 = \dfrac{2(27)}{3}\,\hat{i} + \dfrac{2(9)}{3}\,\hat{j} = \mathbf{18\hat{i} + 6\hat{j}}$
In hydrogen and hydrogen-like (one-electron) atoms, orbitals with the same \(n\) are degenerate — 2s and 2p have the same energy (energy depends only on \(n\)). The statement that 2s energy is less than 2p is only true for multi-electron atoms (due to penetration and shielding). Hence option (3) is wrong for hydrogen-like atoms.
The four advertising objectives correspond to different stages of a product's relationship with consumers:
- Trial: Used for new products — encouraging first-time purchases
- Continuity: Used for products with an established customer base — keeping current users loyal
- Brand Switching: Used when a company wants competitors' customers to switch to its brand
- Switchback: Used to win back former customers who have switched to a competitor
- Reminder Advertising: Used for products in the mature stage of the product life cycle — the product is well known, so the ads simply remind customers it still exists and maintain top-of-mind awareness. Example: Established detergent brands running simple reminder ads year after year.
Advertising budgets are typically highest during the introduction stage and decline gradually as the product matures and develops an established buyer base.
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