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 find the force needed to accelerate the ball, we can use the formula [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.

Here's a step-by-step solution:

1. Identify the Mass and Acceleration:
- Mass of the ball: [tex]\( 140 \)[/tex] grams.
- Acceleration: [tex]\( 25 \)[/tex] m/s[tex]\(^2\)[/tex].

2. Convert Mass to Kilograms:
- Since the standard unit of mass in physics is kilograms, convert the mass from grams to kilograms.
- [tex]\( 140 \)[/tex] grams is equal to [tex]\( 140 / 1000 = 0.14 \)[/tex] kilograms.

3. Plug Values into the Formula:
- Now we use the formula [tex]\( F = ma \)[/tex].
- [tex]\( m = 0.14 \)[/tex] kg and [tex]\( a = 25 \)[/tex] m/s[tex]\(^2\)[/tex].

4. Calculate the Force:
- [tex]\( F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \)[/tex].
- [tex]\( F = 3.5 \)[/tex] Newtons.

Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \)[/tex] N.