Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones

      608.

      609.

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Understanding the Net Change Theorem

       611–619 Use the net change theorem to interpret the given definite integral.

      611. If w´(t) is the rate of a baby’s growth in pounds per week, what does represent?

      612. If r(t) represents the rate at which oil leaks from a tanker in gallons per minute, what does represent?

      613. A new bird population that is introduced into a refuge starts with 100 birds and increases at a rate of p´(t) birds per month. What does represent?

      614. If v(t) is the velocity of a particle in meters per second, what does represent?

      615. If a(t) is the acceleration of a car in meters per second squared, what does represent?

      616. If P´(t) represents the rate of production of solar panels, where t is measured in weeks, what does represent?

617. The current in a wire I(t) is defined as the derivative of the charge, . What does represent if t is measured in hours?

      618. I´(t) represents the rate of change in your income in dollars from a new job, where t is measured in years. What does represent?

      619. Water is flowing into a pool at a rate of w´(t), where t is measured in minutes and w´(t) is measured in gallons per minute. What does represent?

Finding the Displacement of a Particle Given the Velocity

       620–624 A particle moves according to the given velocity function over the given interval. Find the displacement of the particle. Remember: Displacement is the change in position, and velocity is the rate of change in position with respect to time.

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Finding the Distance Traveled by a Particle Given the Velocity

       625–629 A particle moves according to the given velocity function over the given interval. Find the total distance traveled by the particle. Remember: Velocity is the rate of change in position with respect to time.

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628. ,

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Finding the Displacement of a Particle Given Acceleration

       630–632 A particle moves according to the given acceleration function over the given interval. First, find the velocity function. Then find the displacement of the particle. Remember: Displacement is the change in position, velocity is the rate of change in position with respect to time, and acceleration is the rate of change in velocity with respect to time.

      630. , ,

      631. , ,

      632. , ,

Finding the Distance Traveled by a Particle Given Acceleration

       633–635 A particle moves according to the given acceleration function over the given interval. Find the total distance traveled by the particle. Remember: Displacement is the change in position, velocity is the rate of change in position with respect to time, and acceleration is the rate of change in velocity with respect to time.

      633.