Answer :
To solve the problem of finding the force needed to accelerate a ball with a mass of 140 grams at [tex]\( 25 \, \text{m/s}^2 \)[/tex], we can use the formula for force:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
Let's go through the steps:
1. Convert the mass to kilograms:
The mass given is 140 grams. To use it in the formula, it needs to be in kilograms since the acceleration is given in meters per second squared (m/s[tex]\(^2\)[/tex]).
To convert grams to kilograms, divide the mass by 1000:
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
2. Use the formula [tex]\( F = ma \)[/tex] to find the force:
Now, we can substitute the values into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
Multiplying the mass by the acceleration gives us:
[tex]\[ F = 3.5 \, \text{N} \][/tex]
The force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. Therefore, the correct answer is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
Let's go through the steps:
1. Convert the mass to kilograms:
The mass given is 140 grams. To use it in the formula, it needs to be in kilograms since the acceleration is given in meters per second squared (m/s[tex]\(^2\)[/tex]).
To convert grams to kilograms, divide the mass by 1000:
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
2. Use the formula [tex]\( F = ma \)[/tex] to find the force:
Now, we can substitute the values into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
Multiplying the mass by the acceleration gives us:
[tex]\[ F = 3.5 \, \text{N} \][/tex]
The force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. Therefore, the correct answer is 3.5 N.
