Use F = ma when a question is about a force changing an object’s motion. Use momentum = mass × velocity when objects collide or when a question asks about motion before and after an event.
This lesson is part of force and motion. It builds on the acceleration you found in reading motion graphs.
How do I choose the right relationship?
Ask which quantity the question is about. If a force, mass and acceleration appear, use F = ma. If two objects interact and the question gives velocities before and after, use momentum.
Check your textbook for which relationships your form covers, because the depth differs between years. The habits below apply to either.
Worked example 1: force on a trolley
An invented trolley of mass 2.5 kg accelerates at 1.6 m/s² along a bench. Find the resultant force.
Step 1: write the formula. F = ma.
Step 2: substitute with units. F = 2.5 × 1.6.
Step 3: calculate. F = 4.0 N.
The mass is already in kilograms, so no conversion is needed.
Worked example 2: a collision
An invented trolley A of mass 2 kg moves at 3 m/s and hits a stationary trolley B of mass 1 kg. They stick together. Find their common velocity.
Before. Momentum of A = 2 × 3 = 6 kg m/s. Momentum of B = 0. Total = 6 kg m/s.
After. The combined mass is 3 kg, moving at v. Momentum = 3v.
Equate. 3v = 6, so v = 2 m/s.
The combined trolleys move slower than A did, which makes sense because the same momentum is now shared by a larger mass.
The mistake that costs marks
The common slip is to use grams. A student given a mass of 500 g and acceleration 4 m/s² writes F = 500 × 4 = 2 000 N.
The formula needs kilograms. 500 g is 0.5 kg, so F = 0.5 × 4 = 2 N. The wrong answer is 1 000 times too big, which is what the gram-to-kilogram slip always produces.
Check yourself
An invented cart of mass 4 kg moves at 5 m/s and collides with a stationary cart of mass 6 kg. They stick together. Find the velocity after the collision.
Answer
Momentum before = 4 × 5 = 20 kg m/s.
After: combined mass 10 kg, so 10v = 20 and v = 2 m/s.
The velocity is less than 5 m/s because the same momentum is shared by more mass.
What to study next
Move to explaining inertia using safe thought experiments for the conceptual side of the same ideas. Then test yourself with the force and motion practice set.
The mistake log and paper-error review helps you catch unit slips. If you want a teacher to check your choices of formula, see online one-to-one Science tuition.