Answer :
- Convert the mass from grams to kilograms: $m = \\\frac{140}{1000} = 0.14 kg$.
- Apply the formula $F = ma$.
- Calculate the force: $F = 0.14 kg \\times 25 m/s^2 = 3.5 N$.
- The force needed 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 using the formula $F = ma$.
2. Converting Units
First, we need to convert the mass from grams to kilograms since the acceleration is given in meters per second squared. 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
Imagine you're pushing a shopping cart. The heavier the cart (mass), the more force you need to apply to get it moving at the same speed (acceleration). This problem illustrates that relationship: force is directly proportional to mass and acceleration. Understanding this helps in many real-world scenarios, like designing vehicles, calculating the force needed for machines to lift objects, or even understanding how much force you need to throw a ball.
- Apply the formula $F = ma$.
- Calculate the force: $F = 0.14 kg \\times 25 m/s^2 = 3.5 N$.
- The force needed 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 using the formula $F = ma$.
2. Converting Units
First, we need to convert the mass from grams to kilograms since the acceleration is given in meters per second squared. 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
Imagine you're pushing a shopping cart. The heavier the cart (mass), the more force you need to apply to get it moving at the same speed (acceleration). This problem illustrates that relationship: force is directly proportional to mass and acceleration. Understanding this helps in many real-world scenarios, like designing vehicles, calculating the force needed for machines to lift objects, or even understanding how much force you need to throw a ball.
