Problems from Oct 15, 2026

All 12 problems from Oct 15, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.

Physics

Problem 1: A small motor

A motor does $4800$ J of work in $40$ s.

What is its power, in watts?

Answer: 120 W

How it is solved

  1. Power = energy ÷ time: $4800 \div 40$. ($120\ \text{W}$)

Problem 2: Reaction distance

A driver needs $0.7\ \text{s}$ to react and press the brake. The car is moving at $20\ \text{m/s}$ and does not slow down during that time.

How far does the car travel before the brakes start, in metres?

Answer: 14 m

How it is solved

  1. Distance = speed × time: $14\ \text{m}$

Problem 3: Braking distance

A car moving at $20$ m/s brakes steadily, slowing by $5$ m/s every second until it stops.

How far does it travel while stopping?

Answer: 40 m

How it is solved

  1. Use v² = 2 a d
  2. Solve for d: $40\ \text{m}$

Math

Problem 1: Exactly one of two

How many whole numbers from $1$ to $60$ are divisible by exactly one of $4$ or $6$, but not by both?

Answer: 15

How it is solved

  1. Count multiples of $4$: $60 \div 4$ is about $15$, so there are $15$. ($15$)
  2. Count multiples of $6$: $60 \div 6$ is about $10$, so there are $10$. ($10$)
  3. Take out the overlap: Numbers divisible by both are multiples of $12$. There are $5$. Take them out of each list and keep what is in exactly one. ($(15 - 5) + (10 - 5) = 15$)

Problem 2: A map of the coast

A map of a coastline uses a scale of $1 : 50000$. The picture shows two towns on the map.

How far apart are they in real life, in kilometres?

Answer: 2

How it is solved

  1. Real distance in centimetres: $200000\ \text{cm}$
  2. Change to kilometres: $2\ \text{km}$

Problem 3: A shadow and a tree

At noon a child 1.5 m tall casts a shadow 2.4 m long. At the same moment a tree casts a shadow 16 m long.

How tall is the tree?

Answer: 10 m

How it is solved

  1. Spot the similar triangles
  2. Write the ratio
  3. Solve: $10\ \text{m}$

Chemistry

Problem 1: Diluting a solution

$100$ mL of a $2$ M salt solution is mixed with water until the total volume is $400$ mL.

What is the concentration after it is diluted?

Answer: 0.5 M

How it is solved

  1. The amount of dissolved substance stays the same: Moles = concentration × volume, so $2 \times 100 = M_2 \times 400$.
  2. Solve for the new concentration: $M_2 = 2 \times 100 \div 400$. ($0.5\ \text{M}$)

Problem 2: Boiling off water

500 g of salt water is 10% salt by mass. 300 g of water is boiled away.

What is the percent by mass of the solute after the water has gone?

Answer: 25

How it is solved

  1. Solute stays: $50\ \text{g}$
  2. New total: $200\ \text{g}$
  3. Share: $25\%$

Problem 3: Warming a gas

A gas takes up $2$ L at $300$ K and is warmed to $450$ K. The pressure does not change. Temperatures are in kelvin.

What is the new volume, in litres?

Answer: 3 L

How it is solved

  1. Volume is proportional to temperature in kelvin
  2. Solve: $3\ \text{L}$

Electrical engineering

Problem 1: A torch battery

A torch battery holds $2000$ mAh and the torch draws $250$ mA.

For how many hours can it run?

Answer: 8 h

How it is solved

  1. Capacity ÷ current: A battery of $2000$ mAh can supply $2000$ mA for one hour, or less current for longer: $2000 \div 250$. ($8\ \text{h}$)

Problem 2: Heat in a resistor

A current of 2 A flows through a resistor of 5 ohms.

How much power is turned into heat, in watts? (Power = current squared times resistance.)

Answer: 20 W

How it is solved

  1. Square the current
  2. Multiply by the resistance: $20\ \text{W}$

Problem 3: How many switches?

A counter must be able to show every whole number up to $100$.

How many switches (bits) are needed at the very least?

Answer: 7

How it is solved

  1. What $b$ switches can show
  2. Find the smallest b that is enough: $7$