Key takeaways
- Speed = distance ÷ time. Force = mass × acceleration (F = ma).
- Kinetic energy is ½mv², so doubling the speed makes it four times bigger.
- Potential energy near Earth is mgh, with g ≈ 9.81 m/s².
- Convert everything to SI units (m, kg, s) before you calculate.
In this guide
What is physics?
Physics is the science of how things move and interact: why a ball falls, why a car needs brakes, how electricity flows. Physics uses maths to turn these ideas into exact predictions.
Most school physics problems come from a few areas: kinematics (describing motion), dynamics (forces that cause motion), energy and momentum.
Why do physics formulas matter?
They let you predict what will happen before it happens: how long a trip takes, how strong a bridge must be, how far a car travels before it stops.
Kinetic energy depends on speed squared. Double your speed and your car carries four times the energy into a crash.
The key formulas
| Formula | What it finds | Symbols and SI units |
|---|---|---|
v = d ÷ t | Speed | d = distance (m), t = time (s), v in m/s |
a = (v − u) ÷ t | Acceleration | u = start speed, v = end speed (m/s), a in m/s² |
F = m × a | Force | m = mass (kg), a in m/s², F in newtons (N) |
KE = ½ × m × v² | Kinetic energy | v = speed (m/s), KE in joules (J) |
PE = m × g × h | Potential energy | g ≈ 9.81 m/s², h = height (m), PE in J |
p = m × v | Momentum | p in kg·m/s |
How to solve a physics problem step by step
- 1List what you know with units, for example
m = 1,200 kg,a = 2 m/s². - 2Write what you need to find.
- 3Convert to SI units: metres, kilograms, seconds. For km/h to m/s, divide by 3.6.
- 4Choose the formula that links your knowns to the unknown.
- 5Substitute and calculate.
- 6Check the units and size of the answer.
You can check these with the force calculator and the kinetic energy calculator, which show every step.
Energy changes form
A 2 kg rock on a 10 m ledge has potential energy PE = 2 × 9.81 × 10 = 196.2 J. If it falls (ignoring air), that energy turns into kinetic energy. It hits the ground at about √(2 × 9.81 × 10) ≈ 14.0 m/s. This is conservation of energy: energy changes form but the total stays the same. Try it with the potential energy calculator.
Common mistakes to avoid
- Mixing up mass and weight. Mass is in kg. Weight is a force,
W = m × g, in newtons. - Forgetting to square v in kinetic energy.
- Ignoring direction. Velocity and momentum have direction. A ball bouncing back has negative velocity.
- Using the wrong g. On Earth
g ≈ 9.81 m/s². Some books round it to 9.8 or 10, so check which one is expected.
Tips and tricks
- Speed, distance, time triangle: cover the one you need. Distance = speed × time. 150 km in 2 h is
150 ÷ 2 = 75 km/h. - Falling objects: distance fallen from rest is
½gt². In 2 s that is½ × 9.81 × 2² = 19.62 m. Try the free fall calculator. - Collisions: use momentum. A 70 kg runner at 5 m/s has
p = 70 × 5 = 350 kg·m/s.
Where you'll use it in real life
- Driving: stopping distance and why speed limits matter.
- Sport: how hard to kick a ball, or how high a jump can go.
- Home: power ratings of appliances and electricity bills.
- Engineering: designing lifts, bridges, cars and rollercoasters.
Quick summary
Physics problems follow a routine: list what you know, convert to SI units, pick the formula that links knowns and unknowns, then substitute and check the units. Learn the core set: v = d ÷ t, F = ma, KE = ½mv², PE = mgh and p = mv. The free calculators linked above show every step.
Frequently asked questions
What’s the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed plus direction. A car going round a bend at a steady 50 km/h has constant speed but changing velocity.
When do I use energy vs momentum?
Use energy for problems about heights, speeds after falling, springs or work done. Use momentum for collisions and explosions. Some problems need both.
How do I convert km/h to m/s?
Divide by 3.6. For example, 72 km/h ÷ 3.6 = 20 m/s. To go from m/s to km/h, multiply by 3.6.
What is the difference between mass and weight?
Mass is the amount of matter, measured in kg, and is the same everywhere. Weight is the force of gravity on that mass, W = m × g, measured in newtons.
