Newton's laws of motion
The idea
Three short statements connect force to motion and underpin all of mechanics. The first law says an object keeps its velocity — including zero — unless a net force acts on it; motion needs no force to continue, only to change. The second law makes that quantitative: net force equals mass times acceleration, Fnet = ma, so the same push accelerates a small mass more than a large one. The third law says forces come in pairs: if A pushes on B, then B pushes back on A with equal magnitude in the opposite direction.
The key mental discipline is the word NET. An object can have many forces on it and still move at constant velocity, as long as they cancel. When you see acceleration, hunt for the unbalanced leftover after all forces are added with their directions. You already know balanced versus unbalanced forces; the second law just attaches a number to the imbalance.
The classic misconception is that third-law pairs cancel each other. They never do, because the two forces act on different objects: the road pushes the car forward while the car pushes the road backward. Only forces acting on the same object can cancel. If you find yourself canceling an action with its reaction, you have mixed up two different free-body pictures.
Worked example
A 1200 kg car accelerates from rest to 24 m/s in 8.0 s on a straight road. The engine drives the wheels with a forward force of 4500 N. Find the net force on the car and the total resistive force (air drag plus rolling resistance) opposing it.
- Find the acceleration from the velocity change: a = Δv/Δt = (24 − 0)/8.0 = 3.0 m/s², directed forward along the road.
- Apply the second law to get the net force: Fnet = ma = 1200 × 3.0 = 3600 N forward. This is the leftover after all forces are combined, not the engine force itself.
- Set up the force balance along the road: the forward drive force minus the resistive force must equal the net force, so 4500 − R = 3600.
- Solve for the resistance: R = 4500 − 3600 = 900 N pointing backward.
- Sanity-check the picture: the engine supplies more force than the net value because part of it is spent fighting resistance; if drag grew to 4500 N the net force would drop to zero and the car would stop accelerating, exactly as the first law predicts.
Answer. The net force on the car is 3600 N forward, so the resistive forces must total 900 N backward.
Check your understanding
- Why can an object with several forces acting on it still travel in a straight line at constant speed?
- How would you convince a friend that the forces in a third-law pair can never cancel each other out?
- What happens to the acceleration in this problem as the car speeds up and air drag grows, even if the engine force stays the same?
- If you doubled the car's mass but kept the same net force, how would the time to reach 24 m/s change, and why?
Build the foundations first
Newton's laws of motion builds on these concepts. If any feel shaky, start there.