A car is traveling along a road, and its engine is turning over with an angular

Question

A car is traveling along a road, and its engine is turning over with an angular velocity of +220 rad/s. The driver steps on the accelerator, and in a time of 13.0 s the angular velocity increases to +280 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity had remained constant at the initial value of +220 rad/s during the entire 13.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +280 rad/s during the entire 13.0-s interval? (c) Determine the actual value of the angular displacement during the 13.0-s interval.

Explanation / Answer

(a)angular displacement=220*13 =2860 radians
(b)angular displacement=280*13=3640 radians

(c)angular acceleration= (280-220)/13=4.62 radians/s2

so actual angular displacement= (280^2-220^2)/2*4.62 =3246.7 radians

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