Question

The angular acceleration of a wheel is given in rad/s² by 45t³−11t⁴, where t is in seconds. If the wheel starts from rest at t=0.00s, when is the next time the wheel is at rest?

Answer 1

The next time the wheel is at rest is at t = 45/11 seconds.

Step-by-step explanation:

1. To determine when the wheel is at rest, we need to find the values of t at which the angular acceleration is zero. We can do this by setting the given expression for angular acceleration equal to zero and solving for t. 45t³ - 11t⁴ = 0
2. By factoring out t³ from the equation, we get t³(45 - 11t) = 0. Setting each factor equal to zero, we find that t³ = 0 or 45 - 11t = 0.
3. Simplifying the second equation, we have 11t = 45, which gives us t = 45/11.

Therefore, the next time the wheel is at rest is at t = 45/11 seconds.