Given data:
* The initial angular speed of the car is,
[tex]\omega_i=0.54\text{ rad/s}[/tex]* The final angular speed of the car is,
[tex]\omega_f=0.96\text{ rad/s}[/tex]* The angular displacement of the car is,
[tex]\theta=1.4\text{ radians}[/tex]Solution:
By the kinematics equation, the angular acceleration of the car in terms of the angular displacement is,
[tex]\omega^2_{\text{f}}-\omega^2_i=2\alpha\theta[/tex]where,
[tex]\alpha\text{ is the angular acceleration,}[/tex]Substituting the known values,
[tex]\begin{gathered} 0.96^2-0.54^2=2\times\alpha\times1.4 \\ \alpha=\frac{0.96^2-0.54^2}{2\times1.4} \\ \alpha=\frac{0.9216-0.2916}{2.8} \\ \alpha=\frac{0.63}{2.8} \end{gathered}[/tex]By simplifying,
[tex]\alpha=0.225rads^{-2}[/tex]Thus, the angular acceleration of the car is 0.225 radians per second squared.
