Question

1. A particle is moving along a (horizontal) x-axis. Its position as a function of time is given by the equationAt2 B where A-2.10 and B-2.80 and t is in seconds. (i) What are the proper units for A and B in SI units (show your work) (ii) Determine the displacement of the particle during the time interval from -3.00 s to 12 5.00 s. iii) Determine the average velocity (think secant line!) during this time interval (iv) Determine the magnitude of the instantaneous velocity at -5.00 s using both limit function analysis methods that we discussed in class. 2. PV Excursions, LLC offers sightseeing tours of the Prairie View A&M campus and nearby area. One tour, priced at $7 per person, had an average demand of about 1000 customers per week! When the price was lowered to S6, the weekly demand jumped to about 1200 customers!! Assuming that the demand equation is linear, find the tour price that should be charged per person to maximize the total revenue each week. dT 3. The environmental lapse rate, d characterizes the local variation of temperature with elevation in the earth's atmosphere. Atmospheric pressure varies with elevation according to the hydrostatic formula. dz Where M is molar mass (mass per mole), p is molar density (mole per unit volume), and g is the local acceleration of gravity (length per second). Assume that the atmosphere is an ideal gas: PV nRT, where V is volume, n is moles, and R is the ideal gas constant). Assume that the environmental lapse and hydrostatic processes are polytropic meaning that TP constant. Develop an expression for the environmental lapse rte, in terms of M g, R, and δ τ

Answer 1

"x = At^2 + B {A = 2.10 B = 2.80 (i) The units of A & B are A rightarrow m/sec^2 B rightarrow m (ii) at t_1 = 300s x_1 = (2.10 times 9 + 2.8)m t_2 = 5.00 sec x_2 = (2.10 times 25 + 2.8)n so displacement (Delta x) = x_2 -x_1 = 2.10 times 16 = 33.6 m^2 \r\n (iii) average velocity (v^-) = x_2 -x_1/Delta t = 33.6/(5 - 3) = 33.6/2 = 16.3 m/sec v^- = 16.3 m/sec (iv) Instantaneous velocity V_I = d x/dt
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