Posted by **bob** on Friday, April 5, 2013 at 10:54pm.

a particle moves along the x axis in such a way that its acceleration at time t, t>0 , is given by x(t)= (ln x)^2. at what value of t does the velocity of the particle attain its maximum

- ap calculus -
**Anonymous**, Saturday, April 6, 2013 at 5:09am
velocity has max when acceleration is zero

I assume x(t) = (ln t)^2 which is zero at t=1.

- ap calculus -
**MathMate**, Saturday, April 6, 2013 at 9:05am
Assuming the function is

x(t)=(ln(t))^2

then t has a vertical asymptote at x=0.

which explains why the domain of x(t) is set at x>0.

To find the maximum, we need to find

x'(t)=0

where

x'(t)=2ln(t)/t

and x'(t)=0 at t=1.

Check if maximum or minimum by finding x"(t)=2/t^2 - 2ln(t)/t

so

x"(1)=2 >0

Hence t=1 is a minimum.

Therefore, the function has no maximum, as it increases indefinitely as t inreases for t>1.

## Answer This Question

## Related Questions

- calculus - 5. A particle moves along the x-axis in such a way that its position ...
- calculus - a particle moves along the x-axis in such a way that its acceleration...
- Calculus - A particle starts at the point (5,0) at t=0 and moves along the x-...
- calculus - 4. A particle starts at the point (5, 0) at t = 0 and moves along the...
- Calculus - a particle starts at time t = 0 and moves along the x axis so that ...
- calculus - 5. A particle moves along the y – axis with velocity given by v(t)=...
- calculus - A Particle moves along the x-axis so that at any time t>0, its ...
- calculus - Consider a particle moving along the x-axis where x(t) is the ...
- AP CALC. AB - 1.The position of a particle moving on the line y = 2 is given by ...
- Calculus (Answer Check) - A particle moves along the x-axis so that its velocity...

More Related Questions