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If f(t) is measured in meters/second2 and t is measured in seconds, what are the units of meters/second seconds meters2/second meters/second2 meters If f(x) is measured in pounds and x is measured in feet, what are the units of foot-pounds pounds feet feet/pound pounds/foot Explain in words what the integral represents and give units. , where a(t) is acceleration in km/hr2 and t is time in hours. Explain in words what the integral represents and give units. where f(t) is the rate at which the world's population is growing in year t, in billion people per This integral represents between the years of 2005 and 2011. The units of this integral are Explain in words what the integral represents and give units. , where s(x) is rate of change of salinity (salt concentration) in gm/liter per cm in sea water, and where x is depth below the surface of the water in cm.This integral represents the between the surface of the water and a depth of 5 cm. Two cars start from rest at a traffic light and accelerate for several minutes. The figure below shows their velocities as a function of time. Estimate the distance moved by car 1 and 2 during the first minute Estimate the time at which the two cars have gone the same distance Oil leaks out of a tanker at a rate of r = f(t) gallons per minute, where t is in minutes. Write a definite integral expressing the total quantity of oil (in gallons) which leaks out of the tanker in the first four hours. A warehouse charges its customers S5 per day for every 10 cubic feet of space used for storage. The figure records the storage used by one company over a month. How much will the company have to pay? A bicyclist pedals along a straight road with velocity, v, given in the figure below. She starts 2 miles from a lake; positive velocities take her away from the lake and negative velocities take her toward the lake. When is the cyclist farthest from the lake? t = hours Approximately how far away is she at this time? Give a best estimate. (Round your answer to the nearest whole number.) miles The graphs in the figure below represent the velocity, v, of a particle moving along the x-axis for time 0

Explanation / Answer

Q1) You multiply meters/second2 with second inside integral so you get meters/second. Thus it gives velocity.integral of velocity is distance whose units is meters

Ans: (d) meters

Q2) pound is unit of force and integral of force over distance is work whose units are foot-pound

Ans: (a)

Q3) rate of change of velocity is acceleration. thus integral of acceleration is velocity with units km/hr

integral represents change in velocity.

the units of this integral are km/hr

Q4)similar to Q3. the integral in words is the change of population over time.

the integral represents change in population.

the units of integral are billions of people.

Q5) the integral represents Change of salinity with respect to depth of water.

integral represents change in salinity

units of integral are gm/liter

Q6) we have to calculate division by division. Each vertical division is 750 ft/min and each horizontal division is (1/4)min.

First Block: car 1 covers 750 ft in (1/4)min.

car 2 covers approximately (750/4)ft in (1/4) min.

Second Block : car 1 covers (750/2) in next (1/4) min

car 2 covers (750/2-750/4) = (750/4)ft in next (1/4)min (since car 2 starts at (750/4)th vertical division in block2)

Third Block : car 1 covers (750-750/2) = (750/2)ft in next (1/4) min.

car 2 covers (750+750/4-750/4) = 750 ft in next (1/4)min

Fourth Block: car1 covers 750/4 ft in 1/4 min.

car 2 covers 750 ft in 1/4 min.

thus in first minute, distance covered approximately by car 1 is 1687.5ft , car 2 covers 1875ft

  

they would have gone same distance at approximately after (3/4) min and before 1 min.

approximately (3/4)+(1/8) = (7/8)min.

Q7) here integral is done for gallons/minute over minutes. We want for four hours.So converting 4 hours = 4x60min = 240 minutes. the value required is 240.

Q8) the equation of the line can be calculated by first calculating slope as rate of change of cubic feet with respect to days.

(20000-60000)/(30-0) = -4000/3

equation for the line is

cubicfeet = (-4000)/3 * days + 60000. this value of 60000 is obtained as days = 0 , cubic feet =60000.

day = 1, cubic feet = 60000-(4000/3)

day = 2, cubic feet = 60000-(4000/3)*2

.

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day=30,cubic feet=60000-(400/3)*30

total cubic feet used by company = sum of all above = 30*60000-(4000/3)*[1+2+3+...+30]

=18000000-(4000/3)*(465)

=1180000 cubic feet

for every 10 cubic feet company has to pay $5. so total pay = 1180000/10 * 5 = $590000

Q9) total time is 1hour(given from graph). So positive velocity take her away from lake.there are six divisions of time.So each division is 1/6 hour. The most positive velocity is farthest which is achieved after 4th division. So its after 4/6 hour from start.

For every division, the change in velocity is different. thus the distance is

(-10-0)*1/6 + (0-(-10))*1/6 + (20-0)*1/6 + (30-20) *1/6 = 5 miles. But she had started at 2 miles. TOtal distance = 5+2 = 7 miles.

Q10) if change of velocity over time is constant(otherwise called linear) then it has constant acceleration. Thus

(a) V

ends up farthest to left means it has to travel more time with most negative velocity.

(b) IV

ends up farthest means that it has to have highest one side velocity over a period of time so that it goes farthest in one direction. I and II have negative and positive velocities which bring particle to initial position in middle. V has low slope and IV has less velocity over time compared to III. Thus

(c) III

greatest initial acceleration means most slope at start

(d) II

greatest average velocity is given by III (from c)

(e) III

greatest average acceleartion means more positive change of velocity over time.

(f) I

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