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Acceleration, Force, and Mass

A change in an object’s motion—such as Xander speeding up on his scooter—is called acceleration. Acceleration occurs whenever an object is acted upon by an unbalanced force. The greater the net force acting on the object, the greater its acceleration will be, but the mass of the object also affects its acceleration. The smaller its mass is, the greater its acceleration for a given amount of force. Newton’s second law of motion summarizes these relationships. According to this law, the acceleration of an object equals the net force acting on it divided by its mass. This can be represented by the equation:

Calculating Acceleration

This equation for acceleration can be used to calculate the acceleration of an object that is acted on by a net force. For example, Xander and his scooter have a total mass of 50 kilograms. Assume that the net force acting on Xander and the scooter is 25 Newtons. What is his acceleration? Substitute the relevant values into the equation for acceleration:

a=Fm=25 N50 kg=0.5 Nkg

The Newton is the SI unit for force. It is defined as the force needed to cause a 1-kilogram mass to accelerate at 1 m/s2. Therefore, force can also be expressed in the unit kg • m/s2. This way of expressing force can be substituted for Newtons in Xander’s acceleration so the answer is expressed in the SI unit for acceleration, which is m/s2:

a=0.5 Nkg=0.5 kg⋅m/s2kg=0.5 m/s2

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Rej

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