- Identify the given values: \(v_i = 20 \text{ m/s}\), \(v_f = 30 \text{ m/s}\), and \(t = 2.0 \text{ s}\).
- Use the formula for constant acceleration: \(a = \frac{v_f - v_i}{t}\).
- Calculate the change in velocity: \(30 - 20 = 10 \text{ m/s}\).
- Divide by the time interval to find the acceleration: \(a = \frac{10}{2.0} = 5.0 \text{ m/s}^2\), which corresponds to option d.
- Final Answer: \(\boxed{\text{d. } 5.0 \text{ meters/second}^2}\)
Explanation
- Problem Analysis and Definitions
The problem asks us to find the acceleration of a ball that changes its velocity over a specific period of time. We are given the initial velocity \(v_i = 20 \text{ m/s}\), the final velocity \(v_f = 30 \text{ m/s}\), and the time interval over which this change occurs, \(t = 2.0 \text{ s}\). Acceleration is defined as the rate of change of velocity per unit time, which we express as:
\[a = \frac{v_f - v_i}{t}\]
Our objective is to calculate this value and select the correct option from the provided list.
- Calculation and Final Conclusion
To calculate the acceleration, we substitute the known values into our formula:
\[a = \frac{30 \text{ m/s} - 20 \text{ m/s}}{2.0 \text{ s}}\]
First, we find the change in velocity:
\[v_f - v_i = 30 \text{ m/s} - 20 \text{ m/s} = 10 \text{ m/s}\]
Next, we divide this change by the time interval:
\[a = \frac{10 \text{ m/s}}{2.0 \text{ s}} = 5.0 \text{ m/s}^2\]
Thus, the acceleration of the ball is \(5.0 \text{ m/s}^2\). Comparing this result to the given options:
A\(1.6 \text{ m/s}^2\)
B\(3.0 \text{ m/s}^2\)
C\(3.4 \text{ m/s}^2\)
D\(5.0 \text{ m/s}^2\)
The correct option is d.
Examples
Understanding how to calculate acceleration is fundamental in physics and everyday life. For instance, if you are driving a car and press the accelerator pedal, the car's speed increases over time; calculating the rate of this increase helps engineers design safer vehicles and estimate travel times. Similarly, in sports science, coaches use this calculation to measure the explosive speed of athletes as they sprint from a standstill, helping to optimize training programs for better performance on the field.