So the question tells us that a wheel with a diameter of one meter accelerates at a rate of four radiance per second squared. And the first part of the problem wants us to figure out what the final angular velocity is of the wheel at a time T, which is 10 seconds later when were given that the initial angular velocity is to radiance uh, per second. And so to do this, we can use our Kinnah Matic formulas. The one that we're gonna use for a part A is the one that states that the final angular velocity is equal to the initial angular velocity. Plus the acceleration are the angular acceleration times the time. So we know that the initial angular sorry here is the final angular velocity which we're trying to find. We know that the initial angular velocity is to radiance per second plus the, uh, acceleration, which is four times the time, which is 10. So we find that the final, um, angular velocity is equal to 42 radiance per second. So this is the answer to part A. The second part of the problem wants us to figure out what the total angular displacement is equal to. And so to do this, we can just use another kid. A magic formula, which states that the total angular displacement is equal to the initial in your lost e times. The time plus 1/2 times the acceleration times time squares. So we're trying to find this. Tilt the theater here. We know that the initial angular velocity is to times the time, which is 10 plus 1/2 times the acceleration, which is four times the time squared, which is tense, weird. And so if you plug this into a calculator or do you just you could probably just do it in your hand. You'll see that Delta Theta is equal to 220 radiance. So that's the answer to Part B. And lastly, Part C wants us to figure out with the after 10 seconds. What a point on the edge of the ah, the wheel. What it's tangential speed is as well as what the acceleration is of the wheel. So to find a tangential speed, we can take our final, angular velocity, multiply it by the radius of the wheel, and this will give us a tangential velocity so the radius of the wheel is 0.5 meters, right, because the diameter is one meter, so it will just be 42 Radiance per second. Times 0.5 meters gives us 21 meters per second as the tangential velocity. Now, if we want to find the acceleration, there are two places where there's acceleration. There's a tangential acceleration as well as a centripetal acceleration. So to find the tangential acceleration, we can just do the same thing that we did appear for the velocity except will have the angular acceleration times. Uh, the radius is equal to the, um, tangential acceleration. So are angular. Acceleration is for radiance per second squared times the radius which is 0.5 meters and then I give us the conventional acceleration is two meters per second squared now for trying to find what the centripetal acceleration is remembered. This is defined as the, uh tangential velocity squared, divided by the radius squared. So this will be 21 meters per second squared, divided by point five, um, meters. And when you play this to a calculator will get 880 meters per second squared. So now that we have the 10 dental acceleration and the centripetal acceleration, which are perpendicular to each other. We can find the magnitude of the acceleration vector, which is equivalent to the square root of two squared plus 880 squared. And once again, playing this into a calculator gives us a. The magnitude of the acceleration vector is equal to 800 and 82.2 eaters per second squared, and these are your final solutions.