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Physics Problems: maths for physics

Step 5 of 7 in Science Center

Next in your path: 15.4.2 Chemistry Concepts: bonding and reactions

What you'll be able to do
  • Solve physics problems with a repeatable method: list what you know, pick an equation, rearrange it, calculate, and check.
  • Convert units, use SI prefixes and keep the right number of significant figures.
  • Use the constant-acceleration equations for braking, starting and falling problems.
  • Split a projectile's motion into horizontal and vertical parts and find its time in the air, height and range.
  • Draw a free-body diagram and use F = m x a with friction and ramps.
  • Solve work, energy, power, momentum and impulse problems, and check every answer for sense.

Safety first: every activity here uses safe household items. Kids: do them with an adult. Never drop or throw things where people walk or stand, and never test crash ideas with real vehicles or people.

Words in this course 47Open the Vocabulary Hall
01

A method for every problem: units, rearranging and significant figures

In simple words

A physics problem is like a recipe. First you lay out your ingredients (the numbers you are given). Then you pick the right recipe (the equation). Then you cook it (do the maths) and taste it (ask: does this answer make sense?).

Before this course: Physics in Everyday Life: motion, forces, energy (course 15.3). You should know speed = distance / time, Newton's three laws, F = m x a, KE = 1/2 x m x v^2 and PE = m x g x h.

Key facts
  • Five steps for every problem: (1) Draw a sketch and write the given numbers with units. (2) Write the unknown you want. (3) Choose the equation that links them. (4) Rearrange the equation with algebra first, then put in numbers. (5) Check the units and whether the size of the answer makes sense.
  • Rearranging: whatever you do to one side of an equation you do to the other. From v = d / t you get d = v x t and t = d / v. For example, 100 m at 8 m/s takes t = 100 / 8 = 12.5 s.
  • SI prefixes (NIST): nano (n) = 10^-9, micro = 10^-6, milli (m) = 10^-3, centi (c) = 10^-2, kilo (k) = 10^3, mega (M) = 10^6, giga (G) = 10^9. So 3.5 cm = 0.035 m and 5 ms = 0.005 s.
  • Change units before you calculate. Always use metres, kilograms and seconds in formulas. To change km/h to m/s, divide by 3.6: 72 km/h = 20 m/s.
  • Dimensional analysis: the units on both sides of an equation must match. In s = v x t, (m/s) x s = m, so the equation is plausible. If the units do not match, the equation is wrong.
  • Significant figures (OpenStax): in multiplying or dividing, your answer has as many significant figures as the input with the fewest. A circle with radius 1.2 m has area pi x 1.2^2 = 4.5239 m^2, which you report as 4.5 m^2. In adding or subtracting, keep no more decimal places than the least precise number. Zeros that only place the decimal point do not count (0.053 has two significant figures).
  • Do not round in the middle. Keep extra digits on your calculator and round once, at the end.
Step by step
  1. Take this problem: "A cyclist rides 1.8 km in 6.0 minutes. What is the speed in m/s and km/h?"
  2. Write the given numbers and convert: 1.8 km = 1,800 m and 6.0 min = 360 s.
  3. Choose v = d / t and put in numbers: v = 1,800 / 360 = 5.0 m/s.
  4. Convert to km/h by multiplying by 3.6: 5.0 x 3.6 = 18 km/h.
  5. Check the units: m / s gives m/s. Check the size: 18 km/h is a normal cycling speed.
  6. Rearrange v = d / t to find how far the same cyclist goes in 15 minutes (900 s): d = v x t = 5.0 x 900 = 4,500 m.
  7. Check: you can show all five steps for each answer and report two significant figures.
Watch on YouTube
Intro to dimensional analysisKhan Academy India - English · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01A method for every problem: units, rearranging and significant figures
LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:00
Read the video script
[Host at a desk with paper and a calculator] "Every physics problem has the same five steps."
[Text on screen: Given, Unknown, Equation, Solve, Check] "Write what you know, what you want, pick the equation, solve it, then check."
[Screen: 72 km/h divided by 3.6 equals 20 m/s] "Always change units first. To go from kilometres per hour to metres per second, divide by 3.6."
[Text on screen: (m/s) x s = m] "Units must match on both sides. That is a free error check."
[Host] "And do not round until the very end."
Try it now

Write the five steps on a card and keep it. Solve: a runner covers 400 m in 80 s. Find the speed in m/s and km/h, then find how long 1,000 m would take at the same speed. (Answers: 5.0 m/s, 18 km/h, 200 s.)

ClaudeStuck? Copy a ready-made prompt for Claude

Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

I'm learning "Physics Problems: maths for physics" on The Future Market. Lesson 1: "A method for every problem: units, rearranging and significant figures".

What the lesson teaches:
- Five steps for every problem: (1) Draw a sketch and write the given numbers with units. (2) Write the unknown you want. (3) Choose the equation that links them. (4) Rearrange the equation with algebra first, then put in numbers. (5) Check the units and whether the size of the answer makes sense.
- Rearranging: whatever you do to one side of an equation you do to the other. From v = d / t you get d = v x t and t = d / v. For example, 100 m at 8 m/s takes t = 100 / 8 = 12.5 s.
- SI prefixes (NIST): nano (n) = 10^-9, micro = 10^-6, milli (m) = 10^-3, centi (c) = 10^-2, kilo (k) = 10^3, mega (M) = 10^6, giga (G) = 10^9. So 3.5 cm = 0.035 m and 5 ms = 0.005 s.
- Change units before you calculate. Always use metres, kilograms and seconds in formulas. To change km/h to m/s, divide by 3.6: 72 km/h = 20 m/s.
- Dimensional analysis: the units on both sides of an equation must match. In s = v x t, (m/s) x s = m, so the equation is plausible. If the units do not match, the equation is wrong.
- Significant figures (OpenStax): in multiplying or dividing, your answer has as many significant figures as the input with the fewest. A circle with radius 1.2 m has area pi x 1.2^2 = 4.5239 m^2, which you report as 4.5 m^2. In adding or subtracting, keep no more decimal places than the least precise number. Zeros that only place the decimal point do not count (0.053 has two significant figures).
- Do not round in the middle. Keep extra digits on your calculator and round once, at the end.

The exercise I'm working on:
Write the five steps on a card and keep it. Solve: a runner covers 400 m in 80 s. Find the speed in m/s and km/h, then find how long 1,000 m would take at the same speed. (Answers: 5.0 m/s, 18 km/h, 200 s.)

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.
I'm a parent helping my child (about 8 years old) with a lesson called "A method for every problem: units, rearranging and significant figures" from the course "Physics Problems: maths for physics".

Here's what the lesson says:
A physics problem is like a recipe. First you lay out your ingredients (the numbers you are given). Then you pick the right recipe (the equation). Then you cook it (do the maths) and taste it (ask: does this answer make sense?).

The activity:
Write the five steps on a card and keep it. Solve: a runner covers 400 m in 80 s. Find the speed in m/s and km/h, then find how long 1,000 m would take at the same speed. (Answers: 5.0 m/s, 18 km/h, 200 s.)

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.
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My notes
02

Constant acceleration: the four equations

This lesson is part of full access: every course and every level for one payment.

03

Free fall and projectiles: split the motion in two

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04

Forces, free-body diagrams, friction and ramps

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05

Work, energy and power: the shortcut for hard problems

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06

Momentum and impulse: collisions and recoil

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07

Check your answer: estimates, graphs and limits

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++

Final project

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??

Quiz

  1. What are the five steps for solving a physics problem?

  2. What is 72 km/h in m/s?

  3. A radius of 1.2 m gives an area of 4.5239 m^2 from a calculator. How should you report it?

  4. Which constant-acceleration equation do you use when you do not know the time?

  5. A car at 30.0 m/s brakes at 7.00 m/s^2. What is the braking distance?

  6. In projectile motion without air resistance, which direction has constant velocity?

  7. A ball is kicked at 20 m/s at 30 degrees. What are its horizontal and vertical starting speeds?

  8. What launch angle gives the longest range on level ground, ignoring air resistance?

  9. A 100 kg crate has a normal force of 980 N and μs = 0.45. About how much force starts it moving?

  10. What does the work-energy theorem say?

  11. A 60 kg person climbs 3.0 m in 5.0 s. What is the power?

  12. Why does a longer stopping time make the force smaller?

EX

Final exam

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CE

Certificate

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