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A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]$25 \, \text{m/s}^2$[/tex]? (Formula: [tex]F=ma[/tex])

A. 3.5 N
B. 115 N
C. 165 N
D. 4.5 N

Answer :

To determine the force needed to accelerate the ball, we can use the formula for force:

[tex]\[ F = m \times a \][/tex]

where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.

Step-by-step solution:

1. Convert the mass from grams to kilograms:
The mass of the ball is given as 140 grams. To use the standard units in physics, we need to convert this to kilograms.

[tex]\[ 1 \, \text{gram} = 0.001 \, \text{kilograms} \][/tex]

So,

[tex]\[ 140 \, \text{g} = 140 \times 0.001 \, \text{kg} = 0.14 \, \text{kg} \][/tex]

2. Use the formula [tex]\( F = m \times a \)[/tex]:
Now that we have the mass in kilograms, we can plug it into the formula along with the given acceleration.

Given:
- Mass ([tex]\( m \)[/tex]) = 0.14 kg
- Acceleration ([tex]\( a \)[/tex]) = 25 m/s²

Calculate the force:

[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 is [tex]\( 3.5 \, \text{N} \)[/tex].

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