Calculus-1-Net-Change-Integrating-the-Derivative Questions, guaranteed and verified 100%

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Net Change: Integrating the Derivative- HW Problems


The velocity in ft/sec of a particle moving along a line is given below.
Find the displacement and the distance travelled by the particle over
the interval.
1. 𝑣(𝑡) = 𝑡 2 − 4𝑡 + 3, 0≤𝑡≤4
2. 𝑣(𝑡) = 𝑡 2 − 2𝑡 − 8, 1≤𝑡≤5


The acceleration in 𝑚/𝑠𝑒𝑐 2 , initial velocity in 𝑚/𝑠𝑒𝑐, and initial
position are given for a particle moving in a line. Find the velocity at
time 𝑡, the distance travelled over the interval, and the position
function at time 𝑡.
3. 𝑎(𝑡) = 𝑡 − 1, 𝑣 (0) = 4, 𝑠(0) = 2, 0≤𝑡≤5
4. 𝑎(𝑡) = 2𝑡 − 1, 𝑣(0) = −6, 𝑠(0) = 1, 0≤𝑡≤2


5. At time 𝑡 = 0, a storage tank contains 1125 gallons of water.
Water flows out of the tank at a rate of 𝑟(𝑡) = 150 − 10𝑡 gallons per
minute, where 0 ≤ 𝑡 ≤ 15. Find the amount of water that flows out of
the tank over the first 5 minutes. How much flows out when
5 ≤ 𝑡 ≤ 10? How much water is left in the tank after 10min.?


6. The population of a town today is 10,000. The population is
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projected to grow at a rate of 𝑃′ (𝑡) = 100(1 + ), where 𝑡 is in years.
√𝑡
What is the projected change in population over the next 10 years?
What is the projected population 10 years from today?