Using units, show that kg x m/s is equivalent to N x s
1 Newton is 1 kg m/s^2.
(Remember F = m a ?)
Multiply that by 1 s and see what you get
1 Newton is 1 kg m/s^2.
(Remember F = m a ?)
Multiply that by 1 s and see what you get.
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To show that kg x m/s is equivalent to N x s, we need to break down the units and perform the necessary conversions.
Let's start with kg x m/s, which represents the product of kilograms and meters per second.
The unit of force is the newton (N), which is defined as the amount of force required to accelerate a mass of one kilogram by one meter per second squared.
To convert kg x m/s to N x s, we can use the definition of Newton's second law of motion, which states that force (N) is equal to mass (kg) multiplied by acceleration (m/s^2). In equation form, it is expressed as:
Force (N) = mass (kg) x acceleration (m/s^2)
We can rearrange this equation to solve for acceleration:
Acceleration (m/s^2) = Force (N) / mass (kg)
Now, let's substitute the units for these variables:
Acceleration (m/s^2) = (N) / (kg)
Since acceleration is measured in m/s^2, we can rewrite this as:
m/s^2 = N / kg
Next, we need to convert the unit of time from seconds (s) to seconds (s). To do this, we can use the fact that 1 N x s is equivalent to 1 kg x m/s.
Therefore, we can write:
m/s = (N / kg) x s
And rearranging the terms:
N x s = (m/s) x kg
Finally, substituting the units back into the equation:
N x s = (m/s) x kg
Thus, we have shown that kg x m/s is equivalent to N x s.