A car is traveling along a road, and its engine is turning overwith an angular v

Question

A car is traveling along a road, and its engine is turning overwith an angular velocity of +210 rad/s. The driver steps on theaccelerator, and in a time of 9.0 s the angular velocity increasesto +270 rad/s. (a) What would have been theangular displacement of the engine if its angular velocity hadremained constant at the initial value of +210 rad/s during theentire 9.0-s interval? (b) What would have beenthe angular displacement if the angular velocity had been equal toits final value of +270 rad/s during the entire 9.0-s interval?(c) Determine the actual value of the angulardisplacement during the 9.0-s interval.

Explanation / Answer

don't forget to rate, please Assuming the angular velocity is constant at 210 rad/s, there is noangular acceleration, so: = o*t + (1/2)*t2 but, = 0 = *t = (210 rad / s) * (9 s) = 1890radians. Assuming the angular velocity is constant at 270 rad/s, there is noangular acceleration, so: = o*t + (1/2)*t2 but, = 0 = *t = (270 rad/s) * (9s) = 2430radians. Now, assuming the angular velocity does change, then we must solvefor angular acceleration: = o + t (270 rad/s) = (210rad/s) + (9s) = 60/9 rad / s2 And, to solve for : = o*t + (1/2)*t2= (210 rad/s)*9 + (1/2)*(60/9rad/s^2)(9)2 = 2160radians Notice the true value is simply the average of the angulardisplacements from part 1 and 2, respectively.

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