Given that,
Angular velocity = 0.17 rad/s
Angular acceleration = 1.3 rad/s²
Time = 1.7 s
We need to calculate the angular velocity
Using angular equation of motion
![\omega=\omega_{0}+\alpha t](https://tex.z-dn.net/?f=%5Comega%3D%5Comega_%7B0%7D%2B%5Calpha%20t)
Put the value in the equation
![\omega=0.17+1.3\times1.7](https://tex.z-dn.net/?f=%5Comega%3D0.17%2B1.3%5Ctimes1.7)
![\omega=2.38(k)\ m/s](https://tex.z-dn.net/?f=%5Comega%3D2.38%28k%29%5C%20m%2Fs)
We need to calculate the angular displacement
Using angular equation of motion
![\theta=\theta_{0}+\omega_{0}t+\dfrac{\alpha t^2}{2}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Ctheta_%7B0%7D%2B%5Comega_%7B0%7Dt%2B%5Cdfrac%7B%5Calpha%20t%5E2%7D%7B2%7D)
Put the value in the equation
![\theta=0+0.17\times1.7+\dfrac{1.3\times1.7^2}{2}](https://tex.z-dn.net/?f=%5Ctheta%3D0%2B0.17%5Ctimes1.7%2B%5Cdfrac%7B1.3%5Ctimes1.7%5E2%7D%7B2%7D)
![\theta=2.1675\times\dfrac{180}{\pi}](https://tex.z-dn.net/?f=%5Ctheta%3D2.1675%5Ctimes%5Cdfrac%7B180%7D%7B%5Cpi%7D)
![\theta= 124.18^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D%20124.18%5E%7B%5Ccirc%7D)
We need to calculate the velocity at point A
Using equation of motion
![v_{A}=v_{0}+\omega\times r](https://tex.z-dn.net/?f=v_%7BA%7D%3Dv_%7B0%7D%2B%5Comega%5Ctimes%20r)
Put the value into the formula
![v_{A}=0+2.38(k) \times0.2(\cos(124.18)i+\sin(124.18)j))](https://tex.z-dn.net/?f=v_%7BA%7D%3D0%2B2.38%28k%29%20%5Ctimes0.2%28%5Ccos%28124.18%29i%2B%5Csin%28124.18%29j%29%29)
![v_{A}=(-0.267j-0.393i)\ m/s](https://tex.z-dn.net/?f=v_%7BA%7D%3D%28-0.267j-0.393i%29%5C%20m%2Fs)
We need to calculate the acceleration at point A
Using equation of motion
![a_{A}=a_{0}+\alpha\times r+\omega\times(\omega\times r)](https://tex.z-dn.net/?f=a_%7BA%7D%3Da_%7B0%7D%2B%5Calpha%5Ctimes%20r%2B%5Comega%5Ctimes%28%5Comega%5Ctimes%20r%29)
Put the value in the equation
![a_{A}=0+1.3(k)\times0.2(\cos(124.18)i+\sin(124.18)j)+2.38\times2.38\times0.2(\cos(124.18)i+\sin(124.18)j)](https://tex.z-dn.net/?f=a_%7BA%7D%3D0%2B1.3%28k%29%5Ctimes0.2%28%5Ccos%28124.18%29i%2B%5Csin%28124.18%29j%29%2B2.38%5Ctimes2.38%5Ctimes0.2%28%5Ccos%28124.18%29i%2B%5Csin%28124.18%29j%29)
![a_{A}=0.26\cos(124.18)i+0.26\sin(124.18)j+(2.38)^2\times0.2(\cos(124.18)i+\sin(124.18)j)](https://tex.z-dn.net/?f=a_%7BA%7D%3D0.26%5Ccos%28124.18%29i%2B0.26%5Csin%28124.18%29j%2B%282.38%29%5E2%5Ctimes0.2%28%5Ccos%28124.18%29i%2B%5Csin%28124.18%29j%29)
![a_{A}=-0.146j-0.215i−0.636i+0.937j](https://tex.z-dn.net/?f=a_%7BA%7D%3D-0.146j-0.215i%E2%88%920.636i%2B0.937j)
![a_{A}=-0.851i+0.791j\ m/s^2](https://tex.z-dn.net/?f=a_%7BA%7D%3D-0.851i%2B0.791j%5C%20m%2Fs%5E2)
Hence, (a). The velocity at point A is ![(-0.267j-0.393i)\ m/s](https://tex.z-dn.net/?f=%28-0.267j-0.393i%29%5C%20m%2Fs)
(b). The acceleration at point A is ![(-0.851i+0.791j)\ m/s^2](https://tex.z-dn.net/?f=%28-0.851i%2B0.791j%29%5C%20m%2Fs%5E2)