Answer :

Final answer:

The question is asking for the angular deceleration of the automobile engine, given the initial and final velocities and the time frame. The deceleration is found through the formula for acceleration (change in velocity/time), yielding -90.2 rad/s^2, signifying a slowing down.

Explanation:

This question is about calculating the angular deceleration of an automobile engine. Angular deceleration describes the rate at which an object's rotational speed decreases over time.

In this scenario, the engine slows down from 3700 revolutions per minute (rpm) to 1200 rpm in a span of 2.9 seconds (s). To calculate the angular deceleration, you would first need to convert angular velocities from rpm to radians per second (rad/s) by multiplying by 2π/60 because there are 2π radians in one revolution and 60 seconds in a minute.

The initial velocity is 3700 rpm * (2π/60) = 387.3 rad/s and final velocity is 1200 rpm * (2π/60) = 125.7 rad/s. The time is given as 2.9 s. You would then use the formula for acceleration (but in this case deceleration) which is change in velocity divided by time. So the angular deceleration would be (final velocity - initial velocity) / time = (125.7 rad/s - 387.3 rad/s) / 2.9 s = -90.2 rad/s2.

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