Читать книгу Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) - Patrick Jones - Страница 34

493– 497 Solve the given question related to speed or velocity. Recall that velocity is the change in position with respect to time.

493. A mass on a spring vibrates horizontally with an equation of motion given by , where x is measured in feet and t is measured in seconds. Is the spring stretching or compressing at ? What is the speed of the spring at that time?

494. A stone is thrown straight up with the height given by the function , where s is measured in feet and t is measured in seconds. What is the maximum height of the stone? What is the velocity of the stone when it’s 20 feet above the ground on its way up? And what is its velocity at that height on the way down? Give exact answers.

495. A stone is thrown vertically upward with the height given by , where s is measured in feet and t is measured in seconds. What is the maximum height of the stone? What is the velocity of the stone when it hits the ground?

496. A particle moves on a vertical line so that its coordinate at time t is given by for . When is the particle moving upward, and when is it moving downward? Give an exact answer in interval notation.

497. A particle moves on a vertical line so that its coordinate at time t is given by for . When is the particle moving upward, and when it is it moving downward? Give your answer in interval notation.