Answer
$v_A=2.6m/s$, $a_A=9.35m/s^2$
Work Step by Step
We can determine the required velocity and acceleration as follows:
$v_A=\omega r$
$\implies v_A=(5t^2+2)r$
We plug in the known values to obtain:
$v_A=[5(0.5)^2+2](0.8)$
This simplifies to:
$v_A=2.6m/s$
We know that
$a_z=ar=(10t)r=10(0.5)(0.8)=4m/s^2$
and $a_n=(5t^2+2)^2r=[5(0.5)^2+2]^2(0.8)=8.45m/s^2$
Now, $a_A=\sqrt{a_z^2+a_n^2}$
We plug in the known values to obtain:
$a_A=\sqrt{(4)^2+(8.45)^2}$
This simplifies to:
$a_A=9.35m/s^2$
