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Average acceleration is a key concept in kinematics. It describes how the speed of an object changes over time. To calculate it, use the formula:\[a = \frac{v_f - v_i}{t}\]where:

• \(a\) is average acceleration,
• \(v_f\) is final velocity,
• \(v_i\) is initial velocity, and
• \(t\) is the time over which the change occurs.

In our cheetah example, it starts from rest (\(v_i = 0\)), so the equation simplifies to\[a = \frac{v_f}{t}\]Since the problem provides the final speed and distance, not the time, we rely on kinematic equations to find it. This exercise ultimately reveals the average acceleration of the cheetah during its sprint as \(4.44 \, \text{m/s}^2\). Understanding average acceleration helps us see how quickly the cheetah can speed up in real-life scenarios.

Unit conversion is crucial when dealing with physics problems, as it ensures we work with consistent units. In this exercise, you encounter speeds given in kilometers per hour (km/h), while the other measurements are in meters and seconds. This mismatch requires conversion to get accurate results.

Steps for Conversion

To convert speed from km/h to m/s, use the formula:\[v = \frac{v \, (\text{km/h}) \times 1000 \, (\text{m/km})}{3600 \, (\text{s/h})}\]By applying this, let's convert \(72 \, \text{km/h}\) to meters per second:

• Multiply by \(1000\) to switch from km to m.
• Divide by \(3600\) to switch from hours to seconds.

This conversion simplifies to:\[72 \, \text{km/h} \Rightarrow 20 \, \text{m/s}\]Remember to always convert your units before proceeding with calculations. This prevents mistakes and ensures the final answers are correct.

Kinematic equations describe the motion of objects and are essential in solving problems involving acceleration, velocity, and displacement. These equations assume constant acceleration. In our example, we use one of these to find the average acceleration of the cheetah.

Relevant Equation

The kinematic equation used in this solution is:\[d = v_i \cdot t + 0.5 \, a \, t^2\]Here:

• \(d\) is the displacement,
• \(v_i\) is the initial velocity,
• \(a\) is the acceleration, and
• \(t\) is the time.

Since the cheetah starts at rest, \(v_i = 0\), simplifying the equation to:\[d = 0.5 \, a \, t^2\]Using this, we discovered the cheetah's acceleration and calculated the displacement after \(3.5\) seconds. Practicing with such equations will sharpen your ability to analyze complex motion scenarios effectively.