### Home > CALC > Chapter 4 > Lesson 4.4.1 > Problem 4-127

4-127.

As a log falls in a waterfall, its velocity is *v*(*t*) = −32*t*− 18 in feet per second. The position of the log at time*t*= 0 was at the top of the waterfall, 500 feet above sea level. Homework Help ✎Where is the log after 1 second? 2 seconds? 3 seconds?

Where is the log after

*t*seconds? This is the position function*s*(*t*). What is its relationship to*v*(*t*) ?

You need to find the position function, *s*(*t*).

Antidifferentiate *v*(*t*).

Solve for *C*, by evaluating the given point *s*(0)=500.

Check your work: *s*(1) = 466 ft *s*(2) = 400 ft *s*(3) = 302 ft

Refer to the hint in part (a).

Use the eTool below to visualize the problem.

Click the link at right for the full version of the eTool: Calc 4-127 HW eTool