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# Other Applications Involving the Use of Integral of Rates Worksheet

Other Applications Involving the Use of Integral of Rates Worksheet
• 1. A bullet is fired vertically upwards from surface at 25 m / s. Find the height of bullet after 3.5 s?
1. 23.654 m
2. 32.765 m
3. 25.555 m
4. 27.475 m
• 2. If electric current represented as a function of time given by i = 0.5 – 0.4 t, in a calculator circuit. Find the total charge passing from a point in circuit in 0.60 s?
1. 0.45
2. 1.43
3. 0.54
4. 0.05
• 3. A 9.90 nf capacitor having voltage zero in an FM receiver. Calculate the voltage after 3.00 μs if a current i = 0.052 t (in mA) charges the capacitor?
1. 9.94 nV
2. 8.64 nV
3. 6. 74 nV
4. 8.84 nV
• 4. If a car is moving with initial velocity of 7 mph with acceleration a (t) = 3.4 t mph for 10 seconds. Find the velocity of car when 10 seconds are up?
1. 170 mph
2. 171 mph
3. 181 mph
• 5. If a car is moving with initial velocity of 7 mph with acceleration a (t) = 3.4 t mph for 10 seconds. Calculate the distance traveled by car during those 10 seconds?
1. 0.213 mile
2. 0.180 mile
3. 0.120 mile
4. 0.175 mile
• 6. A pump connecting to a generator works at varying rate, depending on amount of  power being drawn from the generator to operate other machinery. The operation rate of the pump is recorded at 5 minute intervals for one hour. Calculate how many gallons were pumped in that hour?
1. 3582.5 gallons
2. 3852.5 gallons
3. 3636.5 gallons
• 7. The total force required for stretching a spring by 3 m beyond its original length is 15 N.m. Calculate the amount of work done to stretch the spring 5 m beyond its original length?
1. 61.5 N.m
2. 55.2 N.m
3. 62.5 N.m
4. 65.2 N.m
• 8. From year 1970 to 1980, the consumption rate of potato in a country was R (t) = 2.2 + 1.1 t millions bushels per year, while ' t ' denotes the years from beginning of 1960. Calculate the consumption of from start of 1972 to the end of 1973?
1. 7.066
2. 8.660
3. 7.9
4. 7. 660
• 9. The acceleration of a moving object is a (t) = t 3 + t, between time interval t = 4 to t = 5, then find the velocity of the body?
1. 28 m / s
2. 20 m / s
3. 37 m / s
4. 27 m / s
• 10. An electron moves in an electric field with acceleration a = - 10 (1 + 4t)- 2, where time 't' is in seconds. Calculate the velocity as a function of time if v = 7.87 inches / s, when t = 0?
1. v = 10 / (1 + 4t) + 7.87 inches s - 1
2. v = 10 / (1 + 4t) + 20 inches s- 1
3. v = 10 / (1 + 4t) inches s - 1
4. v = 10 / (1 + 4t) + 40 inches s- 1
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