High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]