Question 1 The velocity (in m/s) of a rocket is given as a function of time (in seconds). The table below shows the velocity the rocket at specific times. It 0.5 1.2 1.5 1.8 v(t) 213 223 275 300 Use the forward divided difference to approximate the acceleration of the rocket at t=1.2 seconds, with a step size of 0.3 seconds. O 128.3333 O none of the choices O 83.3333 m/s2 O 173.3333 m/s2
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- A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 42 ft/s. Its height in feet after t seconds is given by y=42t-28t^2. a)Find the average velocity for the time period beginning when t=1 second and lasting for the given time. t=.01 s:t=.005 s:t=.002 s:t=.001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. b) Estimate the instanteneous velocity when t=1.Question 7. A manufacturer of jet engines estimates that the rate at which maintainance costs areincurred on its engines is a function of hours of operation of the engine. For one engineused on commercial aircraft, the function is r(t) = 40 + 0.03t2 where t equals the numberof hours of operation and r(t) equals the rate at which repair costs are incurred in dollarsper hour of operation. What are the total maintainance costs expected to equal duringthe first 100 hours of operation? Question 5. The daily total cost(in dollars) incurred by Nando’s for producing q cases of PERi-PERisauce is given by C(q) = −0.11111q3 + 5q2 + 400. How many cases of PERi-PERi sauceshoud be produced to minimize the daily total costIn question 1, assume the acceleration of the object is a(t) = -9.8 meters per second per second. (Neglect air resistance.) A baseball is thrown upward from a height of 2 meters with an initial velocity of 10 meters per second. Determine its maximum height.
- A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G–forces (that is, acceleration in 9.8 – /msec2 increments) versus time after launch.This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.If a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. Therefore, when t = 5, the rate at which the water drains is V'(5)
- A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 35 ft/s. Its height in feet after t seconds is given by y=35t−23t^2A. Find the average velocity for the time period beginning when t=1 and lasting .01 s: .005 s: .002 s: .001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.Estimate the instanteneous velocity when t=1.A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 3.5 days. The average brightness of this star is 2.0 and its brightness changes by ±0.45. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 2.0 + 0.45 sin(2pit/3.5) (a) Find the rate of change of the brightness after t days. dB/dt= (b) Find, correct to two decimal places, the rate of increase after four days. dB/dtA particle that moves along a straight line has velocity v ( t ) = t 2 e − 5 t v ( t ) = t 2 e - 5 t meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
- Two cars leave an intersection at the same time. One is headed south at a constant sped of 30 mi/hr and the other is headed west at a constant spped of 40 mi/hr. a) express the distance d between the cars as a function of t time. b) what is d(6) and what is its interpretation?In the previous Problem Set question, we started looking at the position function s(t)st, the position of an object at time tt . Two important physics concepts are the velocity and the acceleration. If the current position of the object at time tt is s(t)st, then the position at time hh later is s(t+h)st+h. The average velocity (speed) during that additional time hh is (s(t+h)−s(t))hst+h−sth . If we want to analyze the instantaneous velocity at time tt, this can be made into a mathematical model by taking the limit as h→0h→0, i.e. the derivative s′(t)s′t. Use this function in the model below for the velocity function v(t)vt. The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t)at can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=v′(t)=s′′(t)at=v′t=s″t. Problem Set question: A particle moves according to the position function s(t)=e5tsin(7t) Enclose…