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 +209 rad/s. The driver steps on the accelerator, and in a time of 15.9 s the angular velocity increases to +300 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 +209 rad/s during the entire 15.9-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +300 rad/s during the entire 15.9-s interval? (c) Determine the actual value of the angular displacement during the 15.9-s interval.
(a) ? = ? rad
(b) ? = ? rad
(c) ? = ? rad

Explanation / Answer

Time interval   t =   15.9 sec (A) initial velocity   0 = 209 rad /s angular displacement    =   0 *   t     =   (  209 rad /s )( 15.9 sec ) = 3323.1 rad (b) final velocity = 300 rad /sec angular displacement    =   *   t     =   (  300 rad /s )( 15.9 sec ) =4770 rad (c) angular accelaration = change in velocity /time interval       = / t    = ( ( 300 -209 ) / 15.9 ) rad /s^2   = 5.72 rad /s^2 according to kinematic relation 2 - 02 = 2    = (2 - 02 ) / 2   plug all values we get   = 4048.9 rad

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