Answer :
To find the force needed to accelerate the ball, you 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,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-step solution:
1. Identify the given values:
- The mass of the ball is 140 grams.
- The acceleration is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
2. Convert the mass from grams to kilograms:
- Since 1 kilogram equals 1000 grams, divide the mass in grams by 1000 to convert it to kilograms.
[tex]\[
m = \frac{140}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Calculate the force using the formula:
- Multiply the mass in kilograms by the acceleration.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-step solution:
1. Identify the given values:
- The mass of the ball is 140 grams.
- The acceleration is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
2. Convert the mass from grams to kilograms:
- Since 1 kilogram equals 1000 grams, divide the mass in grams by 1000 to convert it to kilograms.
[tex]\[
m = \frac{140}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Calculate the force using the formula:
- Multiply the mass in kilograms by the acceleration.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
