The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion
s = 5 sin(πt) + 2 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]
cm/s
(ii) [1, 1.1]
cm/s
(iii) [1, 1.01]
cm/s
(iv) [1, 1.001]
cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1.
cm/s
+118608 The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion
s = 5 sin(πt) + 2 cos(πt),
where t is measured in seconds. (Round your answers to two decimal places.)
\(s = 5 sin(\pi t) + 2 cos(\pi t)\\ \frac{ds}{dt}=v(t)=5\pi cos(\pi t)-2\pi sin(\pi t)\)
a) Find the average velocity during each time period.
(i) [1, 2] cm/s
\(s(t) = 5 sin(\pi t) + 2 cos(\pi t)\\ s(1) = 5 sin(\pi ) + 2 cos(\pi )=-2\\ s(2) = 5 sin(2\pi ) + 2 cos(2\pi )=0+2=2\\ Average\;\; velocity = \frac{2--2}{2-1} =4cm/sec\)
(ii) [1, 1.1] cm/s
(iii) [1, 1.01] cm/s
(iv) [1, 1.001] cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1.
cm/s
\(v(1)=5\pi cos(\pi )-2\pi sin(\pi )=-5\pi-0=-5\pi\;cm/sec\)
You can do the others yourself :)
