Math

CalculusCalculusVelocity and Acceleration A car travels in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table. t (hours ) 0 0.1 0.2 0.3 0.4 0.5 v (mi/h ) 0 10 20 40 60 50 t (hours ) 0.6 0.7 0.8 0.9 1.0 v (mi/h ) 40 35 40 50 65 (a) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve. (b) Find the open intervals over which the acceleration a is positive. (c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4]. (d) What does the integral ∫ 0 1 v ( t ) d x . signify? Approximate this integral using the Midpoint Rule with five subintervals. (e) Approximate the acceleration at t = 0.8BuyFind*launch*

10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 4, Problem 15PS

Textbook Problem

Velocity and Acceleration A car travels in a straight line for 1 hour. Its velocity *v* in miles per hour at six-minute intervals is shown in the table.

t |
0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |

v |
0 |
10 |
20 |
40 |
60 |
50 |

t |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |

v |
40 |
35 |
40 |
50 |
65 |

(a) Produce a reasonable graph of the velocity function *v* by graphing these points and connecting them with a smooth curve.

(b) Find the open intervals over which the acceleration *a* is positive.

(c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4].

(d) What does the integral

signify? Approximate this integral using the Midpoint Rule with five subintervals.

(e) Approximate the acceleration at *t =* 0.8

Calculus

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In Exercises 109 and 110, determine...Ch. 4.4 - True or False? In Exercises 111 and 112, determine...Ch. 4.4 - Analyzing a Function Show that the function...Ch. 4.4 - Finding a Function Find the function f(x) and all...Ch. 4.4 - Finding Values Let G(x)0x[s0sf(t)dt]ds where f is...Ch. 4.5 - CONCEPT CHECK Analyzing the Integrand Without...Ch. 4.5 - Finding u and du In Exercises 14, complete the...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 526,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - 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Differential Equation In Exercises 2730, solve the...Ch. 4.5 - Slope Field In Exercises 35 and 36, a differential...Ch. 4.5 - Slope Field In Exercises 35 and 36, a differential...Ch. 4.5 - Differential Equation In Exercises 37 and 38, the...Ch. 4.5 - Differential Equation In Exercises 37 and 38, the...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 3342,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - 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Evaluating a Definite Integral In Exercises 7582,...Ch. 4 - Evaluating a Definite Integral In Exercises 7582,...Ch. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Using an Even Function Use 02x4dx=325 to evaluate...Ch. 4 - 86. Respiratory Cycle After exercising for a few...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using a Function Let L(x)=1x1tdt,x0 (a) Find L...Ch. 4 - Parabolic Arch Archimedes showed that the area of...Ch. 4 - Evaluating a Sum and a Limit In Exercises 3 and 4,...Ch. 4 - Evaluating a Sum and a Limit In Exercises 3 and 4,...Ch. 4 - Fresnel Function The Fresnel function S is defined...Ch. 4 - Approximation TheTwo-Point Gaussian Quadrature...Ch. 4 - Extrema and Points of Inflection The graph of the...Ch. 4 - Falling Objects Galileo Galilei (15641642) stated...Ch. 4 - Use the techniques of this chapter to verify this...Ch. 4 - Use the techniques of this chapter to verify this...Ch. 4 - Riemann Sum Use an appropriate Riemann sum to...Ch. 4 - Riemann Sum Use an appropriate Riemann sum to...Ch. 4 - Proof Let f be integrable on [a, b] and 0mf(x)M...Ch. 4 - Using a Continuous Function Let f be continuous on...Ch. 4 - Velocity and Acceleration A car travels in a...Ch. 4 - Proof Prove that if f is a continuous function on...Ch. 4 - Verifying a Sum Verify that i=1ni2=n(n+1)(2n+1)6...Ch. 4 - Sine Integral Function The sine integral function...Ch. 4 - Comparing Methods Let I=04f(x)dx where f is shown...Ch. 4 - Minimizing an Integral Determine the limits of...

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