Location and velocity problem

[OmniXN]

An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?
(b) What is t the first time that the object is at its farthest right?
(c) At the time found in part (b), what is the object's velocity?
(d) At the time found in part (b), what is the object's acceleration?

Thanks so much for looking and would really appreciate some help!

 

[Steven G]

An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?
(b) What is t the first time that the object is at its farthest right?
(c) At the time found in part (b), what is the object's velocity?
(d) At the time found in part (b), what is the object's acceleration?

Thanks so much for looking and would really appreciate some help!

Hi. What have you tried? Where are you stuck? We can guide you but will not do your work for you.

 

[OmniXN]

Hi. What have you tried? Where are you stuck? We can guide you but will not do your work for you.

Hi. I've tried taking the derivative which comes out to x'(t) = 60πcos(20πt). I did not understand how to do part A and B which meant that I was unable to do C and D (as I will need the answer from B to find them)

 

[HallsofIvy]

An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?

What is the period of \(\displaystyle 3 sin(20\pi t)\)? One period is, by definition, the time required for one "back-and-forth" so you need to divide the period into 1 sec.

(b) What is t the first time that the object is at its farthest right?

The largest possible value of sine is 1 so the largest possible value of \(\displaystyle 3 sin(20\pi t)\) is 3. What is the smallest positive value of t so that \(\displaystyle 3 sin(20\pi t)= 3\)?

(c) At the time found in part (b), what is the object's velocity?

You could find the derivative of x(t) and substitute the t value you got for (b). But is the derivative at any maximum value for a function?

(d) At the time found in part (b), what is the object's acceleration?

You will need to find the second derivative of x(t) and evaluate it at the t value you got in t.

Thanks so much for looking and would really appreciate some help!