Posted by **D-MO** on Tuesday, March 11, 2008 at 12:33pm.

A Particle moves along the x-axis so that at any time t>0, its acceleration is given by a(t)= ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is?

The correct answer is 3.346, but how?

- calculus -
**Reiny**, Tuesday, March 11, 2008 at 3:07pm
v(t) = integral (ln(1+2^t)) + c

to integrate ln(1+2^t) escapes me for the moment. I have tried looking it up in tables, but could not find that pattern in my book of integrals. Online integrators could not handle it either.

Hopefully one of the other tutors could shed some light on this one.

- calculus -
**Count Iblis**, Tuesday, March 11, 2008 at 6:10pm
Write it as:

Log[2^(1/2 t + 1)(2^(-1/2 t) + 2^(1/2 t))/2] =

(1/2 t +1) log(2) +

log[cosh(1/2 log(2) t)]

The integral of log(cosh(p t) can be expressed in terms of Barnes G functions of complex arguments using formula 11 of this site:

http://mathworld.wolfram.com/BarnesG-Function.html

Using a partial integration you can express the integral of log(cosh(p t) in terms of the integral of t tanh(pt) and some simple shifts in the integrastion limits will allow you to find the analytical expression.

## 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 ...
- calculus - 5. A particle moves along the x-axis in such a way that its position ...
- 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<...
- Physics - A particle starts from the origin at t = 0 and moves along the ...
- Calculus - The Question: A particle moves along the X-axis so that at time t >...
- Calculus AB - A particle is moving along the x-axis so that at time t its ...
- 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 ...

More Related Questions