Newton’s laws of
motion

Newton’s second law says the acceleration of an object is a = ΣF/m. Net force and mass together set how quickly the velocity changes. Newton’s first law says that if the net force is zero, the velocity stays constant. Newton’s third law says forces come in equal and opposite pairs, and each force in a pair acts on a different object.

In the world

When a car stops suddenly, a passenger keeps moving until a force slows them down. An automotive safety engineer designs the seat belt and the airbag so the stopping force acts over more time. More time means a smaller acceleration for the same change in speed, and a = ΣF/m then means a smaller force on the person. A sprint start uses the third law: the runner pushes back on the blocks, and the blocks push the runner forward with an equal force.

Common mistakes

• A third-law pair does not cancel on the cart. The reaction acts on the other object, so it is not part of the cart’s ΣF.
• Acceleration follows the net force, not the applied push alone. Friction can make ΣF smaller than F_app.
• Zero acceleration does not always mean the cart is stopped. If ΣF is zero and the cart is already moving, it keeps a constant speed.
• Doubling the mass does not double the acceleration. For the same net force, a is cut in half.