A Cheetah, shown in the figure, is the fastest land animals. It could run up to \( 120 \mathrm{~km} / \mathrm{h} \). Starting from rest a Cheetah can reach to a speed of 96.6 \( \mathrm{~km} / \mathrm{h} \) in only three seconds. What is its (a) average acceleration? and (b) average velocity in these 3 seconds?

To find the average acceleration of the cheetah, we can use the formula: \[ \text{Average Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} \] The change in velocity here is from 0 to 96.6 km/h. First, let's convert that speed to meters per second (m/s) for easier calculation: \[ 96.6 \, \text{km/h} = \frac{96.6 \times 1000}{3600} \approx 26.83 \, \text{m/s} \] Now, substituting into the formula: \[ \text{Average Acceleration} = \frac{26.83 \, \text{m/s} - 0 \, \text{m/s}}{3 \, \text{s}} \approx 8.94 \, \text{m/s}^2 \] For the average velocity during the 3 seconds, we can use the formula: \[ \text{Average Velocity} = \frac{\text{Initial Velocity} + \text{Final Velocity}}{2} \] Setting the initial velocity to 0 and the final velocity to 26.83 m/s gives: \[ \text{Average Velocity} = \frac{0 + 26.83 \, \text{m/s}}{2} \approx 13.42 \, \text{m/s} \] So, the average acceleration is approximately \( 8.94 \, \text{m/s}^2 \) and the average velocity over the 3 seconds is about \( 13.42 \, \text{m/s} \).