Saturday

January 31, 2015

January 31, 2015

Posted by **james** on Sunday, February 17, 2013 at 10:13pm.

a.find the acceleration at any time t.

b.find the minimum acceleration of the particle over the interval [0,3]

c.find the maximum velocity of the particle over the interval [0,2]

- ap calc -
**Reiny**, Monday, February 18, 2013 at 12:07amI will read that as

v(t) = (2π - 5)t - sin(πt)

= 2πt - 5t - sin(πt)

a(t) = 2π - 5 - πcos(πt)

for a min of a , a ' (t) = 0

π^2 sin(πt) = 0

sin(πt) = 0

πt = 0 or πt = π or πt = 2π

t = 0 , t = 1 , t = 2

a(0) = 2π - 5 - πcos0 = π - 5

a(1) = 2π - 5 - πcosπ = 2π-5+π = 3π-5

a(2) = 2π - 5 - πcos2π = 2π - 5 - π = π - 5

a(3) = ... = 3π - 5

looks like the min is π-5

c) for max velocity, a(t) = 0

2πt - 5t - sin(πt) = 0

sin (πt) = 2πt - 5t

very messy equation to solve,

I ran it through Wolfram's "magic" webpage and got

t = 0 and t = .670349

so

v(.670349) = 0

v(0) = sin0 = 0

v(2) = (2π-5)(2) - sin 2π

- 2.566.. - 0 = 2.566

check my arithmetic

**Answer this Question**

**Related Questions**

ap calc - a particle moves along the x-axis so that its velocity at any time t ...

calc - i did this problem and it isn't working out, so i think i'm either making...

Calculus (Answer Check) - A particle moves along the x-axis so that its velocity...

Calculus (Answer Check) - A particle moves along the x-axis so that its ...

Calc - a partial moves along the x-axis so that its velocity at time t, for 0<...

math - a particle starts at time t = 0 and moves along the x - axis so that its ...

calculus - 5. A particle moves along the y – axis with velocity given by v(t)=...

Calculus (Answer Check) - Are my answers right? If they are wrong you dont have ...

math - a particle moves with acceleration a(t)=(t-2)m/s^2 along an x axis and ...

Calculus - a particle starts at time t = 0 and moves along the x axis so that ...