Forces and motion: why a loaded cart is harder to accelerate

Imagine giving an empty cart and a loaded cart the same push. Which changes its speed more easily? Keep your prediction in mind.

A force is a push or pull, measured in newtons (N). To predict a cart’s motion, first combine all forces acting on that one cart. Their combined effect is the net force.

Forces in the same direction add: 3 N right and 5 N right give 8 N right. For opposite directions, subtract the smaller magnitude from the larger. The net force points toward the stronger side.

We choose right as positive: F_net = F_right − F_left. Each side means the total force in that direction.

Velocity is speed together with direction. Acceleration tells us how velocity changes each second. Its unit is m/s². A constant rightward acceleration of 2 m/s² changes rightward velocity by 2 m/s every second.

Mass is measured in kilograms (kg). More mass means more inertia: more resistance to changing velocity. Mass is not a force.

Worked example. A 3 kg cart has a 10 N pull right and a 4 N force left.

1. Find the net force: 10 − 4 = 6 N right.
2. Divide by mass: a = 6 / 3 = 2 m/s².
3. State the direction: 2 m/s² right.

If the forces swap directions, F_net = −6 N and a = −2 m/s². The minus sign means left. It does not mean negative mass.

At fixed mass, doubling the net force doubles acceleration. At a fixed nonzero net force, doubling mass halves acceleration. Tripling force triples acceleration; tripling mass reduces it to one third. Halving force halves acceleration; halving mass doubles it.

For example, 6 N on 2 kg gives 3 m/s². Change only the force to 12 N: 6 m/s². Instead, keep 6 N and change mass to 4 kg: 1.5 m/s². Change both to 12 N and 4 kg: 3 m/s² again. What matters is the ratio F_net / m.

Direction needs care. Suppose a cart is travelling right at 3 m/s, but the net force is 4 N left and its mass is 2 kg. Its acceleration is 2 m/s² left, so it initially slows down. If that force continues, it can stop and then reverse.

Acceleration in the direction of travel increases speed. Acceleration against the direction of travel initially decreases speed. Acceleration alone cannot tell you which way the cart is already moving.

Source notes: the physical laws and units follow NASA Glenn’s Newton’s Laws of Motion and The First and Second Laws of Motion. Cart examples and the force lab are idealized teaching models.