Average Speed and Velocity: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Average Speed and Velocity. Understanding the underlying formula is key to arriving at the correct answer below:

Initial velocity \(\vec{v}_i = 30\hat{i}\). Final velocity \(\vec{v}_f = 40\hat{j}\). Time interval \(\Delta t = 10\text{ s}\). Average acceleration \(\vec{a}_{av} = \frac{\vec{v}_f - \vec{v}_i}{\Delta t} = \frac{40\hat{j} - 30\hat{i}}{10} = -3\hat{i} + 4\hat{j}\). The magnitude of average acceleration is \(|\vec{a}_{av}| = \sqrt{(-3)^2 + 4^2} = \sqrt{9+16} = \sqrt{25} = 5\text{ m/s}^2\).