Question
SHOW WORK PLEASE!!!
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 + 3 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
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 + 3 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
Answers
as you know, the average velocity is the integral divided by the time interval. Since the position is the integral of the velocity, the average velocity in [a,b] = (s(b)-s(a))/(b-a)
So, we have
i) (s(2)-s(1))/(2-1) = (2sin2π+3)-(2sinπ+3) = 0
ii) (s(1.1)-s(1))/(1.1-1) = ((2sin1.1π+3)-(2sin.1π+3)))/.1 = -6.18034
and so on
So, we have
i) (s(2)-s(1))/(2-1) = (2sin2π+3)-(2sinπ+3) = 0
ii) (s(1.1)-s(1))/(1.1-1) = ((2sin1.1π+3)-(2sin.1π+3)))/.1 = -6.18034
and so on
a,b,c,d put all the value in the formula than divide the time :
a) figure out s(2) and s(1) than divide
s(2) = 3sin(pi*2) + 4cos(pi2) = 3(0) +4(1) = 4
s(1) = 3sin(pi1) +4cos(pi1) = 3(0) +4(-1) = -4
average velocity is ( s2-s1)/(2-1) = (4- (-4))/ 1 = 8 cm/s
b) {s(1.1) -s(1)}/(1.1 -1) = -7.3 cm/s
c) { s( 1.01)-s(1)}/(1.01-1) = -9.2 cm/ s
d) {s(1.004)-s(1)}/(1.004-1) = -9.3
e) take derivative then put t =1
3picos(pit)-4pisin(pit)
3picos(pi1)-4pisin(pi1)
3pi(-1) = -3pi = -9.42 cm/s
you can estimate t= 1 when they go small interval 1.0005 and so on they will approach to -9.4m/s bylooking
note part b,c,d are the same part a, i just give you an answer but you have to work out like part a to show your works. you just punching in your calculator to figure out your answer by yourself
a) figure out s(2) and s(1) than divide
s(2) = 3sin(pi*2) + 4cos(pi2) = 3(0) +4(1) = 4
s(1) = 3sin(pi1) +4cos(pi1) = 3(0) +4(-1) = -4
average velocity is ( s2-s1)/(2-1) = (4- (-4))/ 1 = 8 cm/s
b) {s(1.1) -s(1)}/(1.1 -1) = -7.3 cm/s
c) { s( 1.01)-s(1)}/(1.01-1) = -9.2 cm/ s
d) {s(1.004)-s(1)}/(1.004-1) = -9.3
e) take derivative then put t =1
3picos(pit)-4pisin(pit)
3picos(pi1)-4pisin(pi1)
3pi(-1) = -3pi = -9.42 cm/s
you can estimate t= 1 when they go small interval 1.0005 and so on they will approach to -9.4m/s bylooking
note part b,c,d are the same part a, i just give you an answer but you have to work out like part a to show your works. you just punching in your calculator to figure out your answer by yourself
s = 4 sin(πt) + 3 cos(πt)