4.7, Summaries of Physics

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4.7 Rectilinear Motion and Other Applications

Example 2: A projectile is fired straight upward with a velocity of 400 feet/second. From physics its distance above the ground after t seconds is s(t) = 16t 2

• 400t. a) Find the time and velocity at which the projectile hits the ground. b) Find the maximum altitude achieved by the projectile. c) Find the acceleration at any time t.

Example 4: An electronics company estimates that the cost (in dollars) of producing x components used in electronic toys is given by C(x) = 200 + 0.05x + 0.0001x 2 . a) Find the cost, the average cost, and the marginal cost of producing 500 units, 1000 units and 5000 units. b) Compare the marginal cost of producing 1000 units with the cost of producing the 1001st unit.

Example 6: The demand for x units of a product is related to a selling price of S dollars per unit by the equation 2x + S 2 12000 = 0. a) Find the demand function, the marginal demand function, the revenue function, and the marginal revenue function. b) Find the number of units and the price per unit that yield the maximum revenue. c) Find the maximum revenue.