University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

385

Pages:

5
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 Assignment: Section 3.4 Enhanced Assignment 1. Find the slope of thefunction's graph at the given point. Then find an equation for the line tangent to the graph there. 3 h(t) = t , (1,1) What is the slope of thefunction's graph at the givenpoint? m= 3 (Simplify youranswer.) Find an equation for the line tangent to the graph at the given point. y= 2. 3t − 2 Find the slope of the tangent to the curve f(x) = 3 x at the point where x = The slope of the tangent to the curve at the given point is − 12 1 4 . . (Simplify youranswer.) 3. A body moves on a coordinate line such that it has a position s = f(t) = t2 − 4t + 3 on the interval 0 ≤ t ≤ 3, with s in meters and t in seconds. a. Find thebody's displacement and average velocity for the given time interval. b. Find thebody's speed and acceleration at the endpoints of the interval. c.When, ifever, during the interval does the body changedirection? Thebody's displacement for the given time interval is −3 m. (Type an integer or a simplifiedfraction.) Thebody's average velocity for the given time interval is (Type an integer or a simplifiedfraction.) −1 Thebody's speeds at the left and right endpoints of the interval are (Type integers or simplifiedfractions.) Thebody's accelerations at the left and right endpoints of the interval are m / s. m / s and 4 2 m / s, respectively. 2 2 m / s and 2 2 m / s , respectively. (Type integers or simplifiedfractions.) hen, ifever, during the interval does the body changedirection? Select the correct choice below and fill in any answer boxes within your W choice. A. The body changes direction at t = 2 s. (Type an integer or a simplifiedfraction.) B. The body does not change direction during the interval. 4. The accompanying figure shows the velocity v = f(t) of a particle moving on a coordinate line. v (a) When does the particle move forward? movebackward? 5 speedup? slowdown? v = f(t) (b) When is theparticle's accelerationpositive? negative?zero? (c) When does the particle move at its greatestspeed? (d) When does the particle stand still for more than aninstant? 1 2 3 4 t (sec) 5 6 7 8 9 10 -5 (a) When does the particle moveforward? 0 < t < 3,5 < t < 8 (Type an equation or a compound inequality. Type an expression using t as the variable. Use a comma to separate answers asneeded.) When does the particle movebackward? 3 9 11. A ball dropped from the top of a building has a height of s = 256 − 16t2 meters after t seconds. How long does it take the ball to reach theground? What is theball's velocity at the moment ofimpact? A. 4 sec, − 128 m/sec B. 4 sec, 128 m/sec C. 8 sec, − 64 m/sec D. 16 sec, − 512 m/sec 2 12. A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t − 5t meters in t seconds. How high does the rockgo? How long does it take the rock to reach its highestpoint? A. 1,428 m, 12 sec B. 2,760 m, 24 sec C. 1,440 m, 24 sec D. 720 m, 12 sec 13. The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3 ft? A. 3π ft2 /ft B. 6π ft2 /ft C. 6 ft2 /ft D. 9π ft2 /ft 14. The driver of a car traveling at 48 ft/sec suddenly applies the brakes. The position of the car is s = 48t − 3t2 , t seconds after the driver applies the brakes. How far does the car go before coming to astop? A. 8 ft B. 384 ft C. 192 ft D. 768 ft 2 15. The driver of a car traveling at 36 ft/sec suddenly applies the brakes. The position of the car is s = 36t − 3t , t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to astop? A. 12 sec B. 18 sec C. 6 sec D. 36 sec