Thursday

January 29, 2015

January 29, 2015

Posted by **Dede** on Wednesday, August 29, 2012 at 1:33pm.

(a)Calculate the weight’s average velocity over the time interval 1 ≤ t ≤ 3. Show clearly how you calculated the average velocity.

(b)Calculate the weight’s average velocity over the time interval 0 ≤ t ≤ π. Show clearly how you calculated the average velocity. (Exact values required!) Explain how this result can be right when the weight is obviously moving all the time!

(c)Explain why the instantaneous velocity of the weight at the instant t = 2 sec cannot be found using only arithmetic and algebra.

(d)Use the connection between average velocity and instantaneous velocity to determine whether the instantaneous velocity of the weight at time t = 2 sec is greater than or less than 0.76 ft/sec. Explain clearly how you decided. (Don’t evaluate a limit or differentiate the cosine to answer this question.)

- Math -
**Steve**, Wednesday, August 29, 2012 at 2:19pmvelocity is

v = dh/dt = -sin(2t)

average v over an interval is

∫[1,3] dv/dt / (3-1)

= 1/2 ∫[1,3] -sin(2t) dt

= 1/2 (1/2 cos 2t) [1,3]

= 1/4 (cos6-cos1)

= 1/4 (.4198) = 0.105

Note that this is just the total displacement / total time

h(pi)-h(0) = .5(1) - .5(1) = 0

after pi seconds, the weight is back where it started. Hence, average velocity = 0, since it has not moved (in effect).

instantaneous velocity is defined as a limit, using cos(2). Trig functions of most integers cannot be evaluated without more advanced techniques.

**Answer this Question**

**Related Questions**

Calculus - The height (in feet) at time t (in seconds) of a small weight ...

algebra 1 help please - 4) a student score is 83 and 91 on her first two quizzes...

Algebra 2 - Solve. 4a-2≤a+1≤3a+4 4a-2-1≤a+1-1≤3a+4-1 4a-...

Pre Calculus - sec x = -2 , π ≤ x ≤ 3π Use a calculator to...

Math - Suppose cosA = 12/13 with 0º≤A≤90º. Suppose also that sinB = ...

Math - Suppose sinA = 12/13 with 90º≤A≤180º. Suppose also that sinB...

Math - Suppose sinA = 12/13 with 90º≤A≤180º. Suppose also that sinB...

Math - Suppose sinA = 12/13 with 90º≤A≤180º. Suppose also that sinB...

PreCalc - I'm not sure how to solve these with calculator. sec x = -2 , π...

Math - Minimize C=7x+3y+4z 0≤x 0≤y 0≤z 100≤2x+3y+3z 120...