Posted by **Anonymous** on Thursday, March 29, 2012 at 6:20pm.

The position of a particle moving in a straight line is given by s(t) = (e^(-t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation:

cos(5T) = 0

5T = arctan(-1/5)

5e^(-t) sin(5t) = 0

tan(5T) = -1/5

cos(5T) = 5

I know that a change in direction will be marked by a change from positive to negative or vice versa, but I don't understand the equations the question gives me. Could someone please talk me through this process to find the right answer?

- Calculus (Related Rates) -
**Steve**, Friday, March 30, 2012 at 10:29am
you are correct, as far as you go. When it changes from pos to neg, it will be zero.

Note that the particle changes direction, not position. So, its velocity changes sign. The velocity is given by the derivative.

s = e^-t cos5t

s' = e^-t (-cos5t - 5sin5t)

so, since e^-t is always positive, we need

-cos5t - 5sin5t = 0

tan 5t = -1/5

## Answer this Question

## Related Questions

- math - For 4.95 seconds , a particle moves in a straight line according to the ...
- math - For 4.95 seconds , a particle moves in a straight line according to the ...
- Calculus - The position of a particle moving on a horizontal line is given by s(...
- calculus - a particle moves along a number line measured in cm so that its ...
- AP Calculus - The position of a particle moving on the x-axis at time t>0 ...
- Physics - A particle moves in a straight line so that its position (x cm) from a...
- Calculus (Derivatives) - Two particles are moving in straight lines. The ...
- Calculus - A particle moves on a vertical line. Its position, s, in metres at t ...
- calculus - velocity of a particle- the displacement s (in meters) of a particle...
- Calculus.. - Two particles are moving in straight lines. The displacement (...

More Related Questions