The kinetic energy KE of an object of mass m moving with velocity v is defined as
(a) Let x = –s(t) be the position function of the object at time t and v(t), a(t) the velocity and acceleration functions. Prove the Work-Energy Theorem by first using the Substitution Rule for Definite Integrals (4.5.5) to show that
Then use Newton’s Second Law of Motion (force = mass × acceleration) and the substitution u = v(t) to evaluate the integral.
(b) How much work (in ft-lb) is required to hurl a 12-lb bowling ball at 20 mi/h? (Note: Divide the weight in pounds by 32 ft/s2, the acceleration due to gravity, to find the mass, measured in slugs.)
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Chapter 5 Solutions
Single Variable Calculus
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning