College

What force is needed to give a 0.25 kg arrow an acceleration of [tex]$196 \, \text{m/s}^2$[/tex]?

A. 0.25 N
B. 49 N
C. 196 N
D. 748 N

Answer :

To find the force needed to give a 0.25 kg arrow an acceleration of [tex]\( 196 \, \text{m/s}^2 \)[/tex], we can use Newton's second law of motion. Newton's second law states that force is equal to mass multiplied by acceleration, which is expressed as the formula:

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

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

Let's break it down:

1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 0.25 kg
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 196 \, \text{m/s}^2 \)[/tex]

2. Plug the values into the formula:

[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]

3. Calculate the force:

[tex]\[ F = 49 \, \text{N} \][/tex]

Therefore, the force needed to give the arrow the specified acceleration is [tex]\( 49 \, \text{N} \)[/tex].