Starting from rest a DVD steadily accelerates to 500 rpm in 1 second, rotates at this angular speed for 3 seconds then steadily decelerates to halt in 2 seconds. How many revolutions does it make?
First, 250 rpm = 250/60 = 4.1666 rps. When acceleration is constant, the average speed is half the sum of initial and final speeds. So you have 1s at 250 rpm for 4.167 revolutions, 3s at 500 rpm for 12.5 revolutions, and 2s at 250 rpm for 8.333 revolutions. Total = 25 revolutions