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)=ðcos(ðt)

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 sinðt + 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 ð 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(t)=...

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

Physics - A particle starts from the origin at t = 0 and moves along the ...

physics - The position of a particle moving along an x axis is given by x = 15t2...

Calculus - At time t >or= to 0, the position of a particle moving along the x...

calculus - A Particle moves along the x-axis so that at any time t>0, its ...

math - The acceleration of a particle at a time t moving along the x-axis is ...

help math - a partial moves along the x-axis so that its velocity at time t, for...

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 ...