an electric motor accelerates a grinding wheel at constant acceleration from 112 rev/min to 295 rev/min in 13 seconds. how many revolutions did it make in this time?
To calculate the number of revolutions made by the electric motor in the given time period, we need to find the average speed of the grinding wheel first. Then we can multiply this average speed by the time to find the total number of revolutions.
The average speed can be calculated by taking the average of the initial and final speeds. In this case, the initial speed is given as 112 revolutions per minute (rev/min), and the final speed is 295 rev/min.
Average speed = (Initial speed + Final speed) / 2
Substituting the given values:
Average speed = (112 rev/min + 295 rev/min) / 2 = 407 rev/min / 2 = 203.5 rev/min
Now, we can calculate the number of revolutions by multiplying the average speed by time:
Number of revolutions = Average speed * Time
Substituting the values:
Number of revolutions = 203.5 rev/min * 13 seconds
To make the units consistent, we need to convert the average speed to revolutions per second:
203.5 rev/min = 203.5 rev/min * (1 min/60 sec) = 3.392 rev/sec
Number of revolutions = 3.392 rev/sec * 13 seconds = 44.096 revolutions
Therefore, the electric motor made approximately 44.096 revolutions in 13 seconds.