While sitting in physics class one day, you begin to ponder the workings of the analog clock on the classroom wall. You notice as the hands sweep in a continuous motion that there are exactly t = 44 minutes left in class.
Through what angle (in radians) will the second-hand turn before the end of class?

The angle turned by the second hand before the end of the class when 44 minutes are passed is;

Angle turned = 276.46 radians

We are given;

Time left for class to end; t = 44 minutes

Now, in a clock it is known that one minute equals 60 seconds and as such the second hand will perform one complete cycle for every minute passed.

Now, we know that;

1 complete cycle = 2π radians.

Thus, for each minute completed in the cycle, the second hand will have completed 2π radians.

Finally, the angle turned by the second hand before the end of the class when 't' minutes are passed is given by the formula:

Angle turned =  Angle per complete cycle × Number of minutes.

Thus;

when t = 44 minutes;

Angle turned = 2π × 44

Angle turned = 276.46 radians

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Angle turned = 276.32 radians

Explanation:

Given:

Time left for the class to end (t) = 44 min

We know that, the second hand performs one complete circle for every minute passed as 1 minute is equal to 60 seconds.

Also, one complete circle is equivalent to 360 degrees or 2π radians.

So, for every minute passed, the second hand completes 2π radians.

Therefore, the angle turned by the second hand when 't' minutes are passed is given as:

Angle turned =  Angle per rotation × Number of minutes.

Angle turned =

Plug in 3.14 for π, 44 for 't' and solve for angle turned. This gives,

Angle turned =

∴ Angle turned = 276.32 radians

a straight line sloped