Answer :
To find out how much force is needed to accelerate a 0.25 kg arrow at a rate of 196 m/s², you can use Newton's second law of motion. This law states that force equals mass times acceleration, which is expressed with the formula:
[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.
Here’s how to solve the problem step-by-step:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 0.25 kg
- Acceleration ([tex]\( a \)[/tex]) = 196 m/s²
2. Apply the formula:
- Substitute the given mass and acceleration into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
- When you multiply 0.25 by 196, you get:
[tex]\[ F = 49 \, \text{N} \][/tex]
Thus, the force needed to give the arrow the specified acceleration is 49 N. This matches the second option in the provided choices.
[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.
Here’s how to solve the problem step-by-step:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 0.25 kg
- Acceleration ([tex]\( a \)[/tex]) = 196 m/s²
2. Apply the formula:
- Substitute the given mass and acceleration into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
- When you multiply 0.25 by 196, you get:
[tex]\[ F = 49 \, \text{N} \][/tex]
Thus, the force needed to give the arrow the specified acceleration is 49 N. This matches the second option in the provided choices.
