The angular speed of an automobile engine is increased at a constant rate from 1200rev/min to 3000rev/min in 12s. How many revolutions does the engine make in this 12s interval?
I worked it out to be 25200 rev. Is that right?
average speed times time: 2100rev/min multiplied by 12/60 min? No way your answer is correct. What is important here is you need to examine how you got that (I know what you did...you did not use units to check to see what came out is in the right units, ie, time divided out).
Oh, I had to find it in rev/min^2.
Er, wait. That is probably wrong. I think I have to go back and convert a few things around.
To find the number of revolutions the engine makes in the given interval of time, we need to use the formula for angular speed, which is:
Angular Speed = Change in angle / Change in time
In this case, the change in angle is the difference between the initial and final angular positions of the engine, and the change in time is the given time interval of 12 seconds.
Given:
Initial angular speed = 1200 rev/min
Final angular speed = 3000 rev/min
Time interval = 12 seconds
We need to convert the angular speeds to radians per second, as revolutions and radians are different angular units. One revolution is equal to 2π radians.
Initial angular speed in radians per second:
1200 rev/min * (2π radians/1 rev) * (1 min/60 s) = 40π radians/sec
Final angular speed in radians per second:
3000 rev/min * (2π radians/1 rev) * (1 min/60 s) = 100π radians/sec
Now let's calculate the change in angle:
Change in angle = Final angular speed - Initial angular speed
Change in angle = 100π radians/sec - 40π radians/sec = 60π radians/sec
Finally, the number of revolutions can be calculated by dividing the change in angle by 2π (since 2π radians represent one revolution):
Number of revolutions = Change in angle / (2π)
Number of revolutions = 60π radians/sec / (2π) = 30 revolutions
Therefore, the engine makes 30 revolutions in the given 12-second interval. So, your calculation of 25200 revolutions seems to be incorrect.