Answer :
Sure! Let's solve the problem step-by-step.
### Problem:
A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex]?
### Given:
- Mass of the ball [tex]\( m = 140 \, g \)[/tex]
- Acceleration [tex]\( a = 25 \, m/s^2 \)[/tex]
### Formula:
The formula to calculate force is:
[tex]\[ F = ma \][/tex]
### Step-by-Step Solution:
1. Convert the mass into kilograms:
Since the mass is given in grams, we need to convert it to kilograms. There are 1000 grams in 1 kilogram.
[tex]\[ 140 \, g = \frac{140}{1000} \, kg = 0.14 \, kg \][/tex]
2. Plug the values into the formula:
Now, using the formula [tex]\( F = ma \)[/tex]:
[tex]\[ F = 0.14 \, kg \times 25 \, m/s^2 \][/tex]
3. Calculate the force:
[tex]\[ F = 0.14 \times 25 \][/tex]
[tex]\[ F = 3.5 \, N \][/tex]
### Answer:
The force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \, N \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{3.5 \, N} \][/tex]
### Problem:
A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex]?
### Given:
- Mass of the ball [tex]\( m = 140 \, g \)[/tex]
- Acceleration [tex]\( a = 25 \, m/s^2 \)[/tex]
### Formula:
The formula to calculate force is:
[tex]\[ F = ma \][/tex]
### Step-by-Step Solution:
1. Convert the mass into kilograms:
Since the mass is given in grams, we need to convert it to kilograms. There are 1000 grams in 1 kilogram.
[tex]\[ 140 \, g = \frac{140}{1000} \, kg = 0.14 \, kg \][/tex]
2. Plug the values into the formula:
Now, using the formula [tex]\( F = ma \)[/tex]:
[tex]\[ F = 0.14 \, kg \times 25 \, m/s^2 \][/tex]
3. Calculate the force:
[tex]\[ F = 0.14 \times 25 \][/tex]
[tex]\[ F = 3.5 \, N \][/tex]
### Answer:
The force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \, N \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{3.5 \, N} \][/tex]
