Answer :
- Convert the mass from grams to kilograms: $m = \frac{140}{1000} = 0.14$ kg.
- Apply the formula $F = ma$.
- Calculate the force: $F = 0.14 \times 25 = 3.5$ N.
- The force needed to accelerate the ball is $\boxed{3.5 N}$.
### Explanation
1. Understanding the Problem
We are given the mass of a ball, $m = 140$ g, and its acceleration, $a = 25$ m/s$^2$. We need to find the force $F$ required to accelerate the ball. The formula relating force, mass, and acceleration is $F = ma$.
2. Converting Units
First, we need to convert the mass from grams to kilograms since the acceleration is given in meters per second squared (m/s$^2$). To convert grams to kilograms, we divide by 1000:$$m (kg) = \frac{m (g)}{1000} = \frac{140}{1000} = 0.14 kg$$
3. Calculating the Force
Now, we can calculate the force using the formula $F = ma$:$$F = ma = (0.14 kg) \times (25 m/s^2) = 3.5 N$$
4. Final Answer
Therefore, the force needed to accelerate the ball at 25 m/s$^2$ is 3.5 N.
### Examples
Understanding the relationship between force, mass, and acceleration is crucial in many real-world scenarios. For example, when designing a car, engineers need to calculate the force required to accelerate the car to a certain speed. Similarly, in sports, understanding this relationship helps athletes optimize their performance, such as calculating the force needed to throw a ball or accelerate during a sprint. This concept is also vital in understanding the motion of objects in physics and engineering.
- Apply the formula $F = ma$.
- Calculate the force: $F = 0.14 \times 25 = 3.5$ N.
- The force needed to accelerate the ball is $\boxed{3.5 N}$.
### Explanation
1. Understanding the Problem
We are given the mass of a ball, $m = 140$ g, and its acceleration, $a = 25$ m/s$^2$. We need to find the force $F$ required to accelerate the ball. The formula relating force, mass, and acceleration is $F = ma$.
2. Converting Units
First, we need to convert the mass from grams to kilograms since the acceleration is given in meters per second squared (m/s$^2$). To convert grams to kilograms, we divide by 1000:$$m (kg) = \frac{m (g)}{1000} = \frac{140}{1000} = 0.14 kg$$
3. Calculating the Force
Now, we can calculate the force using the formula $F = ma$:$$F = ma = (0.14 kg) \times (25 m/s^2) = 3.5 N$$
4. Final Answer
Therefore, the force needed to accelerate the ball at 25 m/s$^2$ is 3.5 N.
### Examples
Understanding the relationship between force, mass, and acceleration is crucial in many real-world scenarios. For example, when designing a car, engineers need to calculate the force required to accelerate the car to a certain speed. Similarly, in sports, understanding this relationship helps athletes optimize their performance, such as calculating the force needed to throw a ball or accelerate during a sprint. This concept is also vital in understanding the motion of objects in physics and engineering.
