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A certain vehicle can accelerate from a standing start to a speed of v(t) = -0.27t2 + 14t feet per second after t seconds (for 0 < t < 30). Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.] D(t) = () Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.) D(10) = ft

A certain vehicle can accelerate from a standing start to a speed of v(t) = -0.27t2 + 14t feet per second after t seconds (for 0 < t < 30). Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.] D(t) = () Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.) D(10) = ft

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.27t² + 14t feet per second after t seconds (for 0 ≤ t < 30). Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.] D(t) = Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.) D(10) = ft
Transcribed Image Text:A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.27t² + 14t feet per second after t seconds (for 0 ≤ t < 30). Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.] D(t) = Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.) D(10) = ft
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