What is the velocity of a particle at t = 5 seconds if its x-position can be modeled by the equation x = 3t^2 + 5?
The derivative of the x-poosition with respect to time will yield the velocity with respect to time. The derivative of the equation is v = 6t, and plugging in 5 for t will yield a velocity of 30 at t = 5.
A cannonball is shot from a cannon at an angle of 40 degrees and at an initial speed of 25 meters per second. The cannonball travels for a period of time. How long does the cannonball travel for and how far away does it land?
Distance = (Initial velocity x time) + .5(acceleration x time^2) and X = (Initial velocity x time) 0 = (25sin(40))t + .5(-9.8)t^2 solves for t = 3.28 s So X = (25cos40)(3.28) for X = 62.82 meters. Therefore the ball traveled 62.82 meters over 3.28 seconds.
If the economy was experiencing a recession, what kind of monetary or fiscal policy could the government pursue to bring the economy back to full employment? Why would these actions help bring the economy back to full employment?
A monetary policy that the government could pursue to bring the economy back to full employment would be to buy bonds on the open market. This would increase the money supply which would in turn decrease the nominal interest rate. By decreasing the nominal interest rate, interest sensitive spending would increase and investment would increase, therefore bringing the economy back to full employment. A fiscal policy that the government could pursue to bring the economy back to full employment would be to cut taxes and/or increase government spending. These actions would shift the aggregate demand curve to the right and bring the economy back to full employment.