At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of –0.40 rad/s^2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What is the angular position of the wheel

at t = 2.0 s? Ans: Theta final=4.5 rad
How do you solve step by step. Thanks
Does this look correct below?
Of = Oi+Wi*t+1/2*a*t^2
Of = 2.3rad+(1.5 rad⁄s(2.0s)+0.5(-0.40 rad⁄s^2)(2.0s)
Of = 2.3 rad + 3.0 rad - 0.8 rad
Of = 4.5 rad
Thanks! Bob Pursley, This helped me solve it and here is the step by step break down.

Step 1: Use the equation for angular position: θf = θi + ωi*t + 1/2*α*t^2

Step 2: Substitute the given values into the equation: θf = 2.3 rad + (1.5 rad/s)*2.0 s + 1/2*(-0.40 rad/s^2)*(2.0 s)^2
Step 3: Simplify the equation: θf = 2.3 rad + 3.0 rad - 0.8 rad
Step 4: Calculate the final angular position: θf = 4.5 rad

Yes, the equation you've written is correct. The equation you used to solve for the final angular position is:

θf = θi + ωi*t + (1/2)*α*t^2

Let's break it down step by step:

1. Identify the given quantities:
- Initial angular position (θi) = 2.3 rad
- Initial angular velocity (ωi) = 1.5 rad/s
- Angular acceleration (α) = -0.40 rad/s^2
- Time (t) = 2.0 s

2. Substitute the given values into the equation:
θf = 2.3 rad + (1.5 rad/s * 2.0 s) + (0.5 * -0.40 rad/s^2 * (2.0 s)^2)

3. Simplify the equation using the correct order of operations:
θf = 2.3 rad + 3.0 rad - 0.8 rad
θf = 4.5 rad

So the final angular position of the wheel at t = 2.0 s is 4.5 rad.

Great job on solving the problem!

To find the angular position of the wheel at t = 2.0 s, you can use the equation:

θf = θi + ωi * t + (1/2) * α * t^2

Given:
θi = 2.3 rad (initial angular position)
ωi = 1.5 rad/s (initial angular velocity)
α = -0.40 rad/s^2 (constant angular acceleration)
t = 2.0 s (time)

Substitute the given values into the equation:

θf = 2.3 rad + (1.5 rad/s) * 2.0 s + (1/2) * (-0.40 rad/s^2) * (2.0 s)^2

Simplify the equation by performing the calculations:

θf = 2.3 rad + 3.0 rad - 0.8 rad

θf = 4.5 rad

Therefore, the angular position of the wheel at t = 2.0 s is 4.5 rad.