section 3.7 hw

Current Score : 67 / 67 Due : Friday, March 28 2014 11:59 PM EDT

1. 11/11 points | Previous Answers SCalcET7 3.7.001.

A particle moves according to a law of motion where t is measured in seconds and s in feet.

(a) Find the velocity at time t.

(b) What is the velocity after 5 s?

(c) When is the particle at rest?

t = 4 s (smaller value)

t = 6 s (larger value)

(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.)

(e) Find the total distance traveled during the first 7 s. 120 ft

(f) Find the acceleration at time t.

Find the acceleration after 5 s.

(g) Graph the position, velocity, and acceleration functions for

Section 3.7 HW (Homework)Frances CoronelMAT 151 Calculus I, Spring 2014, section 01, Spring 2014Instructor: Ira Walker

WebAssign

The due date for this assignment is past. Your work can be viewed below, but no changes can be made.

Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you haveviewed the answer key. Automatic extensions are not granted if you have viewed the answer key.

View Key

s = f(t), t ≥ 0,

f(t) = t3 − 15t2 + 72t

v(t) =

v(5) = -3 ft/s

t

a(t) =

a(5) = 0 ft/s2

0 ≤ t ≤ 7.

FVCproductions

(h) When is the particle speeding up? (Enter your answer in interval notation.)

When is it slowing down? (Enter your answer in interval notation.)


A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet.

(a) Find the velocity at time t (in ft/s).

v(t) =

(b) What is the velocity after 2 s? v(2) = -.28 ft/s


t = 0 s (smaller value)

t = 15/4 s (larger value)

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)

(e) Find the total distance traveled during the first 12 s. (Round your answer to two decimal places.) 122.28 ft

(f) Find the acceleration at time t (in ft/s2).

Find the acceleration after 2 s.

f(t) = 0.01t4 − 0.05t3

a(t) =

a(2) = -.12 ft/s2

http://www.webassign.net/web/Student/Assignment-Responses/last?dep=8337847#

(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 12.

(h) When is the particle speeding up? (Enter your answer using interval notation.)

When is it slowing down? (Enter your answer using interval notation.)


A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet.

(a) Find the velocity at time t (in ft/s).

v(t) =

(b) What is the velocity after 3 s? (Round your answer to two decimal places.)v(3) = .118 ft/s


f(t) = te−t/4


t = 4 s

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)

(e) Find the total distance traveled during the first 10 s. (Round your answer to two decimal places.)2.12 ft

(f) Find the acceleration at time t (in ft/s2).

Find the acceleration after 3 s. (Round your answer to three decimal places.)

(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 10.

(h) When is the particle speeding up? (Enter your answer using interval notation.)

When is it slowing down? (Enter your answer using interval notation.)

a(t) =

a(3) = -.1476 ft/s2



Graphs of the velocity functions of two particles are shown, where t is measured in seconds.

(a)

When is the particle in figure (a) speeding up? (Enter your answer using interval notation.)

When is the particle in figure (a) slowing down? (Enter your answer using interval notation.)

(b)

When is the particle in figure (b) speeding up? (Enter your answer using interval notation.)

When is the particle in figure (b) slowing down? (Enter your answer using interval notation.)



Graphs of the position functions of two particles are shown, where t is measured in seconds.

(a)

When is the particle in figure (a) speeding up? (Enter your answer using interval notation.)

When is the particle in figure (a) slowing down? (Enter your answer using interval notation.)

(b)

When is the particle in figure (b) speeding up? (Enter your answer using interval notation.)

When is the particle in figure (b) slowing down? (Enter your answer using interval notation.)



A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 16 mm and itwants to know how the area of a wafer changes when the side length x changes. Find

Explain the meaning of in this situation.


(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i) 3 to 4

(ii) 3 to 3.5

(iii) 3 to 3.1

(b) Find the instantaneous rate of change when r = 3.

A'(3) =

A(x) A'(16).

A'(16) = 32 mm2/mm

A'(16)

represents the rate at which the area is increasing with respect to the side length as A reaches 32 mm2.

represents the rate at which the area is increasing as x reaches 32 mm.

represents the area as the side length reaches 16 mm.

represents the rate at which the side length is increasing with respect to the area as x reaches 16 mm.

represents the rate at which the area is increasing with respect to the side length as x reaches 16 mm.

A'(16)

A'(16)

A'(16)

A'(16)

A'(16)




A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. Find the rate at which the area withinthe circle is increasing after each of the following.

(a) after 2 s

cm2/s

(b) after 5 s

cm2/s

(c) after 7 s

cm2/s


(a) The volume V of a growing spherical cell is where the radius is measured in micrometers (1 µm = 10−6m). Find the

average rate of change of V with respect to r when r changes from 2 to each of the following. (Round your answers to one decimal place.)

(i) 2 to 5 µm

163.36 µm3/µm

(ii) 2 to 3 µm

79.547 µm3/µm

(iii) 2 to 2.1 µm

52.794 µm3/µm

(b) Find the instantaneous rate of change of V with respect to r when r = 2 µm. (Round your answer to one decimal place.)

V'(2) = 50.24 µm3 / µm

V = πr3,43



10.5/5 points | Previous Answers SCalcET7 3.7.017.

The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x2 kg. (See this example.)

(a) Find the linear density when x is 4 m.24 kg/m

(b) Find the linear density when x is 5 m.30 kg/m

(c) Find the linear density when x is 9 m.54 kg/m

Where is the density the highest?

Where is the density the lowest?

11.6/6 points | Previous Answers SCalcET7 3.7.018.MI.

If a tank holds 5500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V ofwater remaining in the tank after t minutes as

Find the rate at which water is draining from the tank after the following amounts of time. (Remember that the rate must be negativebecause the amount of water in the tank is decreasing.)

(a) 5 min-198 gal/minMaster ItIf a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives thevolume V of water remaining in the tank after t minutes as

Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must benegative because the amount of water in the tank is decreasing.)

5 minPart 1 of 2

The rate at which the volume V(t) changes is given by V'(t). For we have the following.

At the right end of the rod.

At the left end of the rod.

In the middle of the rod.

At the right end of the rod.

At the left end of the rod.

In the middle of the rod.

V = 5500 1 − t 0≤ t ≤ 50.150

2

V = 4000 1 − t 0≤ t ≤ 50.150

2

V(t) = 4000 1 − t ,150

2

V'(t) = (No Response)

http://www.webassign.net/scalcet7/3-3-ex-02-alt.gif


(b) 10 min-176 gal/minMaster ItIf a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives thevolume V of water remaining in the tank after t minutes as


10 minPart 1 of 1As found earlier, the rate at which the water drains is given by

When t = 10, the rate at which the water drains is, therefore,

gal/min.

(c) 20 min-132 gal/minMaster ItIf a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives thevolume V of water remaining in the tank after t minutes as




gal/min.

(d) 50 min0 gal/minMaster ItIf a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives thevolume V of water remaining in the tank after t minutes as




V = 4000 1 − t 0≤ t ≤ 50.150

2

V'(t) = −160 1 − t .150

V'(10) = (No Response)

V = 4000 1 − t 0≤ t ≤ 50.150

2

V'(t) = −160 1 − t .150


V = 4000 1 − t 0≤ t ≤ 50.150

2

V'(t) = 160 1 − t .150


gal/min.

At what time is the water flowing out the fastest?t = 0 min

At what time is the water flowing out the slowest?t = 50 minMaster ItIf a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives thevolume V of water remaining in the tank after t minutes as

At what time is the water flowing out the fastest?

At what time is the water flowing out the slowest?Part 1 of 2Looking that the values of at different times, we see that the water is flowing out the fastest at the (No Response) , when

12.3/3 points | Previous Answers SCalcET7 3.7.019.

The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t (measured in seconds) is given by

[See this example. The unit of current is an ampere 1 A = 1 C/s.]

(a) Find the current when t = 0.5 s.4.75 A

(b) Find the current when t = 1 s.5 A

At what time is the current the lowest?t = 2/3 s


V = 4000 1 − t 0≤ t ≤ 50.150

2

V'(t)t = (No Response) min.

Q(t) = t3− 2t2 + 6t + 2.


http://www.webassign.net/scalcet7/3-7-ex-03-alt.gif


section 3.7 hw

Documents