During a speed change on a record player from 45 rpm to 33 rpm, how many revolutions does the record make in 2.7 seconds?

To determine how many revolutions the record makes during a speed change from 45 rpm (revolutions per minute) to 33 rpm in a duration of 2.7 seconds, we first need to find the average speed of the record during the transition.

1. Calculating average speed: The initial speed is 45 rpm and the final speed is 33 rpm. The average speed can be calculated as follows:

[

\text{Average speed} = \frac{\text{Initial speed} + \text{Final speed}}{2} = \frac{45 , \text{rpm} + 33 , \text{rpm}}{2} = \frac{78}{2} = 39 , \text{rpm}

]

2. Converting rpm to rps: To work with the time in seconds, convert the average speed from revolutions per minute to revolutions per second:

[

39 , \text{rpm} = \frac{39}{60} , \text{rps} \approx 0.65 , \text{rps}

]

3. **Calculating revolutions in 2