91Ó°ÊÓ

A person skis down a slope with an acceleration (in \(\mathrm{m} / \mathrm{s}^{2}\) ) given by \(a=\frac{600 t}{\left(60+0.5 t^{2}\right)^{2}},\) where \(t\) is the time (in \(\mathrm{s}\) ). Find the skier's velocity as a function of time if \(v=0\) when \(t=0\)

Find the areas bounded by the indicated curves. $$y=3 \sqrt{x+1}, x=0, y=6$$

Find the indicated moment of inertia or radius of gyration. Find the radius of gyration of a plate covering the first-quadrant region bounded by \(y^{2}=1-x\) with respect to the \(x\) -axis.

Find the areas bounded by the indicated curves. $$y=2 / \sqrt{x}, x=0, y=1, y=4$$

Find the coordinates of the centroids of the given figures. In Exercises \(11-22,\) each region is covered by a thin, flat plate. The region bounded by \(y=4-x\) and the axes

A 1500 -lb elevator is suspended on cables that together weigh 12 Ib/ft. How much work is done in raising the elevator from the basement to the second floor, a distance of \(24 \mathrm{ft} ?\)

If a car decelerates at \(250 \mathrm{m} / \mathrm{s}^{2}\) (about the maximum a human body can survive) during an accident, and the car was going at \(96 \mathrm{km} / \mathrm{h}\) at impact, over what distance must an airbag stop a person in order to survive the crash?

Find the volume generated by revolving the regions bounded by the given curves about the \(x\) -axis. Use the indicated method in each case.$$y=x^{2}+1, x=0, x=3, y=0 \quad (disks)$$

Find the indicated moment of inertia or radius of gyration. Find the radius of gyration of a plate covering the region bounded by \(y=x^{2}, x=3,\) and the \(x\) -axis with respect to the \(x\) -axis.

A chain is being unwound from a winch. The force of gravity on it is \(12.0 \mathrm{N} / \mathrm{m}\). When \(20 \mathrm{m}\) have been unwound, how much work is done by gravity in unwinding another \(30 \mathrm{m} ?\)