Learn: what changes a cart’s motion?
Imagine a 2 kg cart already rolling to the right. You push it with a force of 10 newtons to the right, while friction pushes with 4 newtons to the left. The cart’s acceleration depends on the combined effect of those forces.
Words and units you need
- A force is a push or pull arising from an interaction. Its unit is the newton, N.
- Mass, m, is measured in kilograms (kg). It describes how strongly an object resists a change in velocity.
- Velocity includes speed and direction. Acceleration, a, is the rate at which velocity changes, measured in metres per second per second (m/s²).
- Net force means the vector sum of all external forces on your chosen object. In a one-dimensional example, choose a positive direction and add signed values.
First law: zero net force means constant velocity
In an inertial reference frame, an object with zero net external force has constant velocity. It can be at rest or moving at a constant speed in a straight line. This does not mean “there are no forces.” A stationary book can have its weight downward balanced by the table’s upward force.
When a car slows, a passenger’s body tends to continue its earlier motion. A seat belt supplies a force that changes that motion. Inertia is the tendency to maintain velocity; it is not an extra forward force.
Second law: add forces before dividing by mass
For constant mass, Fnet = ma. Choose right as positive for the cart.
- Identify the object: the 2 kg cart.
- Add horizontal forces: Fnet = +10 N − 4 N = +6 N.
- Divide by mass: a = Fnet/m = 6 N ÷ 2 kg = 3 m/s² rightward.
- Interpret: while these forces stay constant, rightward velocity increases by 3 m/s each second. The vertical forces balance in this level-track model.
Explore: push, resistance and acceleration
Keep mass at 2 kg and the leftward resistance at 4 N. Change the push to see the instantaneous net force and acceleration. The cart is already moving right in each case; this model does not simulate stopping or a change in friction after reversal.
Push 10 N; net force +6 N; acceleration +3 m/s² (right).
At a 4 N push, the horizontal forces balance: acceleration is zero even though the cart is moving. With less than 4 N push, acceleration is leftward; a right-moving cart slows at that instant. A leftward acceleration does not by itself mean leftward velocity.
Third law: name both objects
When your foot pushes backward on the ground, the ground pushes forward on your foot. The two forces have equal magnitude and opposite directions, and act simultaneously on different objects. They do not cancel when finding the net force on your body alone.
For a book on a table, the table’s upward force on the book pairs with the book’s downward force on the table. The book’s weight pairs with the book’s gravitational pull on Earth. Weight and the table’s force on the book may balance, but they are not a third-law pair because they act on the same object.
Practice: explain before calculating
1. A 3 kg object has 9 N rightward and 3 N leftward forces. Find its acceleration.
Right positive: Fnet = 9 − 3 = 6 N. Then a = 6/3 = 2 m/s² rightward.
2. A puck moves in a straight line at constant velocity. Must its net force point forward?
No. Constant velocity means zero acceleration, so the net force is zero in this inertial-frame model.
3. A swimmer pushes a wall. What is the third-law partner?
The wall’s force on the swimmer. One force acts on the wall and the other on the swimmer; both belong to the same interaction.
4. Double the mass while keeping the same nonzero net force. What happens to acceleration?
From a = Fnet/m, doubling m halves a. A 6 N net force gives 3 m/s² for 2 kg and 1.5 m/s² for 4 kg.
Review: object, forces, motion
Choose the object. Draw only forces acting on that object. Add them with directions, then use mass to find acceleration. Keep force pairs on different objects separate from forces that balance on one object. Newtonian mechanics is a model for ordinary motion; these examples assume speeds far below the speed of light.
Optional explanations: OpenStax on inertia and third-law pairs. Continue with AP Physics 1.