Please, please, please, Help me!?

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin πt + 5 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????
Estimate the instantaneous velocity of the particle when t = 1.
Your help would be appreciated! Thank you

Question

Please, please, please, Help me!?

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin πt + 5 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????
 Estimate the instantaneous velocity of the particle when t = 1.
 Your help would be appreciated! Thank you

luigi0210 · Answer

$$\LARGE \mathbb{\color{navy}{WELCOME~TO~OPENSTUDY}}$$

compassionate · Answer

[One moment]

compassionate · Answer

$$V= ds/dt$$
$$f \prime (s) = 3\cos (\pi t) - 5 \sin (\pi t)$$
$$average velocity = \sum_{}^{} V / n$$

$$V= f \prime (s)$$
since cos 180 = -1 and sin 180 = 0 the equation change : $$f \prime = 3t$$
i) t = 1.2 seconds  $$f \prime = 3t = 3 \times 1.2 = 3.6$$
ii) like the above
III) like the above
iv) like the above

and finally you get the average velocity by : $$f' i + f' ii + f' iii + f' iv /6$$

compassionate · Answer

[Not original work. Courtesy of OpenStudy]