Answer :
Answer:
Velocity = 22 m/s
Acceleration = 968 m/s^2
Tangential component of acceleration = 12 m/s^2
Explanation:
The kinematic expression is:
[tex]dw=\alpha dt\\dw=(3t^{2} +12)dt[/tex]
integrating the expression when w =12 rad/s and t=0, we have:
[tex]\int\limits^w_y {dw} \,=\int\limits^2_0 {3t^{2}+12 } \, dt\\ w-12=t^{3} +12t|2-0\\w-12=2^{3} +12*2\\w=44rad/s[/tex]
The velocity at point A is:
[tex]v_{A} =wr_{A} =44*0.5=22m/s[/tex]
α at t=2s is:
[tex]\alpha =3t^{2} +12=3(2^{2} )+12=24rad/s^{2}[/tex]
The normal component of acceleration at point A is equal to:
[tex]a_{A} =w^{2} r_{A} =44^{2} *0.5=968m/s^{2}[/tex]
The tangential component of acceleration at point A is:
[tex]\alpha _{A} =\alpha r_{A} =24*0.5=12m/s^{2}[/tex]