Question: A ball with the inital velocity of $25$ m/s [W,] is hit which changes it's velocity to $29$ m/s [E], in $0.25$ seconds, what is the balls average accelration
1. **State the problem:**
We need to find the average acceleration of a ball whose velocity changes from $25$ m/s west to $29$ m/s east in $0.25$ seconds.
2. **Understand the directions and velocities:**
West and East are opposite directions. Let's assign East as positive and West as negative.
Initial velocity, $v_i = -25$ m/s (since it's west)
Final velocity, $v_f = +29$ m/s (since it's east)
3. **Formula for average acceleration:**
$$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}$$
4. **Calculate the change in velocity:**
$$\Delta v = v_f - v_i = 29 - (-25) = 29 + 25 = 54 \text{ m/s}$$
5. **Calculate average acceleration:**
$$a_{avg} = \frac{54}{0.25}$$
6. **Simplify the fraction:**
$$a_{avg} = \frac{54}{\cancel{0.25}} \times \frac{\cancel{1}}{0.25} = 216 \text{ m/s}^2$$
7. **Interpretation:**
The average acceleration is $216$ m/s$^2$ towards the east (positive direction).