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pls help me!

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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

Jan 26, 2018
edited by Guest  Jan 26, 2018

#1
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+1

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 :)

Jan 26, 2018