Homework Help: Calculus AB

Posted by Savannah on Friday, January 20, 2012 at 5:33pm.

A particle is moving along the x-axis so that at time t its acceleration is
a(t)=đcos(đt)
At time t=1/2, the velocity v of the particle is 1/2.

Find the velocity of the particle at any time t. I think I got that right, as sinđt + C.

Now it wants the minimum velocity of the particle. How do I find that?

Calculus AB - Savannah, Friday, January 20, 2012 at 5:34pm
Ugh the pi symbol didn't work. All of the đ should be pi. so it would be a(t) = picos(pit)

and my answer should be sin(pit) + C
Calculus AB - Reiny, Friday, January 20, 2012 at 6:31pm
a(t) = π cos(πt)
v(t) = sin (πt) + c . where v(t) is velocity
when t=1/2, v(1/2) = 1/2

1/2 = sin (π/2) + c
1/2 = 1 + c
c = -1/2

v(t) = sin (πt) - 1/2
for a min of v(t) , v'(t) = 0 , that is, a(t) = 0

πcos(πt) = 0
cos(πt) = 0
πt = π/2 or πt = 3π/2
t = 1/2 or t = 3/2

we already know v(1/2) = 1/2
we need
v(3/2) = sin(3π/2) - 1/2
= -1 - 1/2 = -3/2

so the minimum velocity is -3/2

Answer this Question

Related Questions

calculus - 5. A particle moves along the y – axis with velocity given by v(...
Calculus - a particle starts at time t = 0 and moves along the x axis so that ...
Calculus-particle motion - 1. A particle is moving on the x-axis (or any number ...
Calculus - I don't understand what the graph is suppose to show and what the...
Calculus - At time t >or= to 0, the position of a particle moving along ...
math - The acceleration of a particle at a time t moving along the x-axis is ...
calculus - A Particle moves along the x-axis so that at any time t>0, its...
Calc - A particle moves along the x-axis in such a way that it's position in...
calculus - A particle is moving along the x- axis so that its velocity at any ...
physics - The position of a particle moving along an x axis is given by x = 15t2...

For Further Reading

First Name:
School Subject:
Answer: