High School

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 calculate the force needed to accelerate a ball with a mass of 140 grams at an acceleration of 25 [tex]\(m/s^2\)[/tex], we use the formula:

[tex]\[ F = ma \][/tex]

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

Here's a step-by-step solution:

1. Convert Mass to Kilograms:
The mass of the ball is given in grams, but we need to use kilograms in our calculations because the standard unit of mass in the formula is kilograms (kg).
[tex]\[ 1 \text{ kg} = 1000 \text{ grams} \][/tex]
So, convert 140 grams to kilograms:
[tex]\[ 140 \text{ grams} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \][/tex]

2. Apply the Formula:
Now that we have the mass ([tex]\(m\)[/tex]) in kilograms, we can multiply it by the acceleration ([tex]\(a\)[/tex]) to find the force:
[tex]\[ F = m \times a \][/tex]
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 \][/tex]

3. Calculate the Force:
[tex]\[ F = 3.5 \text{ N} \][/tex]

So, the force needed to accelerate the ball is [tex]\(3.5 \text{ N} \)[/tex].

Among the given options, the correct answer is:
[tex]\[ 3.5 \text{ N} \][/tex]