+0  
 
0
9
16441
1
avatar

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 4 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)

(a) Find the average velocity during each time period.

i. [1,2]

ii. [1,1.1]

iii. [1.1.01]

iv. [1.1.001]

(b) Find the instaneous velocity of the particle when t=1

Guest Mar 5, 2015

Best Answer 

 #1
avatar+93342 
+5

 

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 4 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)

(a) Find the average velocity during each time period.

i. [1,2]

$$\\s(1)=2sin(\pi *1)+4cos(\pi *1)\\
s(1)=2sin(\pi)+4cos(\pi)\\
s(1)=0+4*-1\\
s(1)=-4\\\\
\\s(2)=2sin(\pi *2)+4cos(\pi *2)\\
s(2)=2sin(2\pi)+4cos(2\pi)\\
s(2)=0+4*+1\\
s(2)=4\\\\
Average\; velocity=\frac{distance}{time}\\
Average\; velocity=\frac{4--4}{2-1}\\
Average\; velocity=\frac{8}{1}\\
Average\; velocity=8 \;cm/sec$$

ii. [1,1.1]

iii. [1.1.01]

iv. [1.1.001]

 

(b) Find the instaneous velocity of the particle when t=1

 

$$\\s=2sin(\pi t)+4cos(\pi t)\\
v(t)=\frac{ds}{dt}=2\pi cos(\pi t)+-4\pi sin(\pi t)\\
v(t)=\frac{ds}{dt}=2\pi cos(\pi t)-4\pi sin(\pi t)\\
v(1)=2\pi cos(\pi*1 )-4\pi sin(\pi *1)\\
v(1)=2\pi *-1 \quad -4\pi *0\\
v(1)=-2\pi \;\;cm/sec\\$$

Melody  Mar 6, 2015
 #1
avatar+93342 
+5
Best Answer

 

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 4 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)

(a) Find the average velocity during each time period.

i. [1,2]

$$\\s(1)=2sin(\pi *1)+4cos(\pi *1)\\
s(1)=2sin(\pi)+4cos(\pi)\\
s(1)=0+4*-1\\
s(1)=-4\\\\
\\s(2)=2sin(\pi *2)+4cos(\pi *2)\\
s(2)=2sin(2\pi)+4cos(2\pi)\\
s(2)=0+4*+1\\
s(2)=4\\\\
Average\; velocity=\frac{distance}{time}\\
Average\; velocity=\frac{4--4}{2-1}\\
Average\; velocity=\frac{8}{1}\\
Average\; velocity=8 \;cm/sec$$

ii. [1,1.1]

iii. [1.1.01]

iv. [1.1.001]

 

(b) Find the instaneous velocity of the particle when t=1

 

$$\\s=2sin(\pi t)+4cos(\pi t)\\
v(t)=\frac{ds}{dt}=2\pi cos(\pi t)+-4\pi sin(\pi t)\\
v(t)=\frac{ds}{dt}=2\pi cos(\pi t)-4\pi sin(\pi t)\\
v(1)=2\pi cos(\pi*1 )-4\pi sin(\pi *1)\\
v(1)=2\pi *-1 \quad -4\pi *0\\
v(1)=-2\pi \;\;cm/sec\\$$

Melody  Mar 6, 2015

14 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.