+0

# pls help me!

0
234
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.)

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

Guest Jan 26, 2018
edited by Guest  Jan 26, 2018
#1
+92933
+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 :)

Melody  Jan 26, 2018

### 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.