Finding Average Speed in Free Fall

The problem asks for the average speed of a ball dropped from rest and falling for 2 seconds under gravity. We are given the acceleration due to gravity, \(g = 10 \text{ m/s}^2\). Since the ball is dropped, its initial velocity (\(u\)) is 0 m/s.

Calculating Final Velocity

We first calculate the final velocity (\(v\)) after 2 seconds using the first equation of motion:

\( v = u + at \)

Here:

• Initial velocity, \(u = 0 \text{ m/s}\)
• Acceleration, \(a = g = 10 \text{ m/s}^2\)
• Time, \(t = 2 \text{ s}\)

Substituting the values:

\( v = 0 + (10 \text{ m/s}^2)(2 \text{ s}) \)

\( v = 20 \text{ m/s} \)

Calculating Average Speed

For motion with constant acceleration, the average speed (\(v_{avg}\)) is the mean of the initial and final velocities:

\( v_{avg} = \frac{u + v}{2} \)

Substituting the initial (\(u=0\)) and final (\(v=20 \text{ m/s}\)) velocities:

\( v_{avg} = \frac{0 \text{ m/s} + 20 \text{ m/s}}{2} \)

\( v_{avg} = \frac{20 \text{ m/s}}{2} \)

\( v_{avg} = 10 \text{ m/s} \)

Therefore, the average speed of the ball during the 2 seconds of free fall is 10 m/s.