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Answer :
Sure! Let's solve the problem step-by-step.
Question:
A ball has a mass of 140 grams. What is the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex]?
Solution:
1. First, understand the formula to use:
The formula for force is [tex]\( F = m \cdot a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
2. Convert the mass to kilograms:
The mass given is 140 grams. Since the standard unit of mass in physics is kilograms (kg), we need to convert grams to kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
Thus,
[tex]\[
\text{mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Apply the given acceleration:
The acceleration [tex]\( a \)[/tex] is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
4. Calculate the force using the formula:
Now we use the formula [tex]\( F = m \cdot a \)[/tex] with the mass in kilograms and the acceleration.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
5. Perform the multiplication:
[tex]\[
F = 0.14 \times 25 = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
Answer:
[tex]\[
3.5 \, \text{N}
\][/tex]
Question:
A ball has a mass of 140 grams. What is the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex]?
Solution:
1. First, understand the formula to use:
The formula for force is [tex]\( F = m \cdot a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
2. Convert the mass to kilograms:
The mass given is 140 grams. Since the standard unit of mass in physics is kilograms (kg), we need to convert grams to kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
Thus,
[tex]\[
\text{mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Apply the given acceleration:
The acceleration [tex]\( a \)[/tex] is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
4. Calculate the force using the formula:
Now we use the formula [tex]\( F = m \cdot a \)[/tex] with the mass in kilograms and the acceleration.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
5. Perform the multiplication:
[tex]\[
F = 0.14 \times 25 = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
Answer:
[tex]\[
3.5 \, \text{N}
\][/tex]
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