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Solving force and motion problems

Students solve multi-step force and motion problems using F = ma and a = Δv ÷ t with correct units, use a graph to support a quantitative argument, and check answers for reasonableness (AC9S10U05, node 7, a practise node).

Year 10 Physics · Newton's laws · about 20 minutes · Open the student lesson

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

Students will be able to

Timing

Engage 3 min · Explain 12 min · Evaluate 3 min · Typical adds 1 min, Wider about 1 min

Before class

A practice lesson with no simulation, following Free body diagrams. Set the width with ?width=minimum, typical (default) or wider. The Year 10 progression marks this node as a place for structured practice, so students need pencil and calculator more than a screen: ask them to show each line in their books before entering an answer.

Answers with a sign are entered as numbers (−2.5). Round figures are chosen for clean numbers; real braking and engine forces vary with speed.

Running the lesson

  1. Engage: tally the predictions. Ask the 'acceleration' group what force the acceleration depends on.
  2. Explain: the five-step routine is the success criterion; collect a different problem from each group.
  3. In your own words: the routine and the motorbike problem.

The hard part (on purpose)

Choosing the step, not just the formula. When a student reaches for a number, ask what quantity it is and which step it belongs to.

When students get stuck

What you will seeA question to askThe fix
A student uses the engine force alone.What other force acts, and which way?Resistance, backwards. F in F = ma is the net force.
A student gets a huge or tiny answer.Does a mass in grams or a time in minutes appear anywhere?Convert to kg and s first.

Answers to the checks

  1. Engage: which step first?: A 1500 kg car has an engine force of 4000 N forwards and a resistance of 1000 N backwards. You are asked how fast its speed is changing. What do you work out first?
    The net force, 3000 N. Acceleration depends on the net (unbalanced) force, not the engine force alone. Then a = F ÷ m = 3000 ÷ 1500 = 2 m/s².
  2. Net force: A 1500 kg car has an engine force of 4000 N and a resistance of 1000 N. What is its acceleration (m/s²)?
    2
    Net force = 4000 − 1000 = 3000 N. a = F ÷ m = 3000 ÷ 1500 = 2 m/s².
  3. Speed after 6 s: It accelerates at 2 m/s² from rest. What is its speed after 6 s (m/s)?
    12
    Δv = a × t = 2 × 6 = 12 m/s.
  4. Braking: A 1200 kg car travelling at 20 m/s brakes to a stop in 8 s. What is its acceleration (m/s²)? Use a negative sign for slowing down.
    -2.5
    a = Δv ÷ t = (0 − 20) ÷ 8 = −2.5 m/s².
  5. Braking force: What braking force does the 1200 kg car need (N)? Give the size only.
    3000
    F = ma = 1200 × 2.5 = 3000 N.
  6. Is it reasonable: A student calculates the braking force of a car as 3 000 000 N. What should they do?
    Check the working: a force that large is not reasonable for a family car
    Compare the answer with what you know: a family car's braking force is a few thousand newtons. A huge number suggests a unit slip (grams for kilograms, for example).
  7. The graph: A speed–time graph for a trolley is a straight line rising from 0 m/s at 0 s to 6 m/s at 3 s. What is the acceleration, and what does the gradient show?
    2 m/s²: the gradient of a speed–time graph is the acceleration
    Gradient = change in speed ÷ change in time = acceleration. Steeper means a bigger acceleration.
  8. Elaborate: two-step problem: A 60 kg sprinter reaches 9 m/s from rest in 3 s. What net force acts on the sprinter (N)?
    180
    a = 9 ÷ 3 = 3 m/s². F = ma = 60 × 3 = 180 N.
  9. Elaborate: school zones: A car's stopping distance at 60 km/h is about 36 m, and at 40 km/h about 20 m. What is the best argument for a 40 km/h school-zone limit?
    At the lower speed the car stops in much less distance, and the force on anyone it hits is smaller
    A quantitative argument uses numbers: going 50% faster (60 instead of 40 km/h) takes nearly twice the distance to stop, and a faster car has more energy to lose.

Stretch and support

Stretch: A 1000 kg car has a braking force of 5000 N while travelling at 30 m/s. How long does it take to stop, and how far does it go? (6 s; 90 m, the area under the speed–time graph.)

Support: Give a five-line template (Known, Net force, Acceleration, Speed or time, Reasonable?) with the first line filled in.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient science coach for a Year 10 student in Australia. Help me understand ONE idea only, from the lesson "Solving force and motion problems".

The idea: Quantitative problem solving — integrating all three laws: I can solve multi-step force and motion problems that require selecting and applying Newton's laws, using mathematical representations including graphs and algebraic formulas.

What understanding looks like:
- Solves a multi-step problem applying at least two of Newton's laws with correct units throughout
- Uses mathematical representations (graphs or algebraic formulas) to support a quantitative argument
- Checks the reasonableness of a calculated answer in physical terms

Mistakes students often make here:
- A student uses the engine force alone.
- A student gets a huge or tiny answer.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- If I seem to be missing the idea that comes before this one (Multi-force analysis and free body diagrams), check it quickly, then come back.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Solving force and motion problems".

Exit ticket

A 50 kg skateboarder is pushed with a net force of 100 N from rest. How fast is she moving after 4 s?

a = 100 ÷ 50 = 2 m/s². After 4 s: 2 × 4 = 8 m/s.

What each step is for

Where it leads

Next: Newton's laws in the real world.

In class: collect braking data with a toy car and a ramp; use a speed–time graph from a data logger; work through a vehicle's stopping distance table.