If a fist is 25g and it takes 400N of force to crack a board how fast will you have to accelerate your arm to crack the board?
Impulse=change of momentum
Force*time=mass*change in velocity
So I guess this assumes the final velocity of the hand is zero. The question is still flawed, however, it should be asking how fast does your hand have to hit the board to crack it?
Acceleration is an entirely different thing.
Use F=ma
remember to convert the mass to kg.
By the way a fist has a mass much greater than 25 g.
I can't imagine a fist weighing only 25 g. That is less than one ounce. Are you sure you copied that problem correctly?
Anyway, the equation to use is F = m a. Solve for a. It is a deceleration, not an acceleration, by the way. Also, it the acceleration of the fist that matters, not the entire arm.
Another thing that is wrong with your question is the implication that all you need is a certain force to break the board. It will depend upon how long the force is applied. There is a complicated problem of dynamic bending involved.
Whatever school district or homeschool/online text you are using does not seem to be doing a good job.
To determine how fast you would have to accelerate your arm to crack the board, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = m * a.
In this case, the force required to crack the board is 400 N. However, we need to calculate the mass of the fist to use in the equation. Let's assume the fist has a density similar to water (1000 kg/m³). We can convert the fist's mass from grams to kilograms by dividing by 1000.
Mass of the fist = 25 g / 1000 = 0.025 kg
Now we can rearrange the equation to solve for acceleration:
a = F / m
a = 400 N / 0.025 kg
a ≈ 16,000 m/s²
Therefore, you would need to accelerate your arm at approximately 16,000 meters per second squared to crack the board.