How To Use Newtons To Calculate Meters Per Second

Newtons are the standard unit for force in physics. Newton's second law states that the force required to accelerate a mass by a given extent is given by the product of these two quantities:

\(F=ma\)

Mass has units of kilograms (kg) while acceleration has units of meters per second squared, or m/s².

In some physics problems, you may be given the magnitude of a force, the mass of an object on which that force has been acting, and the time in seconds that has elapsed since the force began acting on the object, which is presumed to be at rest initially. To solve such a problem, you need to have access to the basic equations of motion in mathematical physics, specifically, the one that states:

\(v=v_0+at\)

where v is velocity at time t.

For example, assume a force of 100 N has acted on a 5-kg toy car for 3 seconds. How fast is the car moving at this point, assuming no friction is present?

Since you know that F = ma, F = 100 N and m = 5 kg,

\(100=5a\implies a = 20\text{ m/s}^2\)

Substitute the acceleration you just calculated into the kinematic equation given above, with the initial velocity v₀ equal to zero:

\(v=v_0+at=0+20\times 3 = 60\text{ m/s}\)

You may find it interesting to convert meters per second to miles per hour, since the latter is a more everyday and intuitive unit in the United States. Since 1 mile = 1,609.34 m and 1 hour = 3,600 s, converting m/s to miles/hr requires multiplying by 3600/1,609.34, which equals 2.237.

Thus for this problem, you have 60 m/s × 2.237 = 134.2 miles/hr.