Unit Conversion Practice

Quiz: Unit Conversion Practice

This quiz follows Lesson 2: Unit Conversions and Their Importance from the course Time, Speed & Distance: Core Concepts for Competitive Exams.

In speed–distance–time problems, the single most common source of error is mixing units. A speed given in km/h cannot be multiplied directly by a time given in seconds, and a distance in metres cannot be divided by a speed in km/h without conversion first.

What you will practise

The conversion factor between km/h and m/s: multiply by ##\dfrac{5}{18}## to go from km/h to m/s, and by ##\dfrac{18}{5}## to go the other way.
Converting distance units (km ↔ m, cm ↔ m).
Converting time units (hours ↔ minutes ↔ seconds).
Keeping units consistent before applying ##\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}##.
Real-life conversion examples such as vehicle speeds and travel times.

Tip: Always convert first, then calculate. Work through each question carefully — the difficulty level is moderate.

Q1. To convert a speed given in km/h into m/s, you should multiply it by which factor?

##\dfrac{5}{18}##

##\dfrac{18}{5}##

##\dfrac{1}{1000}##

##\dfrac{1000}{3600}##

Since ##1\ \text{km} = 1000\ \text{m}## and ##1\ \text{h} = 3600\ \text{s}##, we get ##1\ \text{km/h} = \dfrac{1000}{3600}\ \text{m/s} = \dfrac{5}{18}\ \text{m/s}##. So multiply by ##\dfrac{5}{18}##.

Q2. A car travels at ##72\ \text{km/h}##. What is its speed in m/s?

##10\ \text{m/s}##

##20\ \text{m/s}##

##25\ \text{m/s}##

##30\ \text{m/s}##

Multiply by ##\dfrac{5}{18}##: ##72 \times \dfrac{5}{18} = 4 \times 5 = 20\ \text{m/s}##.

Q3. A cyclist moves at ##5\ \text{m/s}##. What is this speed in km/h?

##12\ \text{km/h}##

##15\ \text{km/h}##

##18\ \text{km/h}##

##25\ \text{km/h}##

To go from m/s to km/h, multiply by ##\dfrac{18}{5}##: ##5 \times \dfrac{18}{5} = 18\ \text{km/h}##.

Q4. How many metres are there in ##2.5\ \text{km}##?

##250\ \text{m}##

##2500\ \text{m}##

##25000\ \text{m}##

##25\ \text{m}##

Since ##1\ \text{km} = 1000\ \text{m}##, we have ##2.5 \times 1000 = 2500\ \text{m}##.

Q5. Convert ##450\ \text{m}## into kilometres.

##0.045\ \text{km}##

##0.45\ \text{km}##

##4.5\ \text{km}##

##45\ \text{km}##

Divide by ##1000##: ##450 \div 1000 = 0.45\ \text{km}##.

Q6. How many seconds are there in ##1.5## hours?

##90\ \text{s}##

##150\ \text{s}##

##5400\ \text{s}##

##900\ \text{s}##

##1\ \text{hour} = 3600\ \text{s}##, so ##1.5 \times 3600 = 5400\ \text{s}##.

Q7. Express ##45## minutes in hours.

##0.45\ \text{h}##

##0.75\ \text{h}##

##1.33\ \text{h}##

##0.25\ \text{h}##

Divide by ##60##: ##45 \div 60 = 0.75\ \text{h}##.

Q8. A train covers ##90\ \text{km}## in ##1## hour. Its speed in m/s is:

##15\ \text{m/s}##

##20\ \text{m/s}##

##25\ \text{m/s}##

##30\ \text{m/s}##

Speed ##= 90\ \text{km/h}##. Converting: ##90 \times \dfrac{5}{18} = 5 \times 5 = 25\ \text{m/s}##.

Q9. A speed of ##36\ \text{km/h}## equals how many m/s?

##6\ \text{m/s}##

##10\ \text{m/s}##

##12\ \text{m/s}##

##18\ \text{m/s}##

##36 \times \dfrac{5}{18} = 2 \times 5 = 10\ \text{m/s}##.

Q10. A runner covers ##100\ \text{m}## in ##20\ \text{s}##. What is the speed in km/h?

##18\ \text{km/h}##

##20\ \text{km/h}##

##36\ \text{km/h}##

##5\ \text{km/h}##

Speed ##= \dfrac{100}{20} = 5\ \text{m/s}##. Converting: ##5 \times \dfrac{18}{5} = 18\ \text{km/h}##.

Q11. Why must units be made consistent before using ##\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}##?

Because the formula only works for km and hours

Because mixing units gives a numerically wrong answer

Because speed has no units

Because distance is always in metres

The formula assumes distance and time are in matching units. Mixing km with seconds, for example, produces a meaningless result, so units must be converted first.

Q12. A car travels ##150\ \text{km}## in ##2## hours. What is its speed in m/s?

##20.83\ \text{m/s}##

##75\ \text{m/s}##

##41.67\ \text{m/s}##

##12.5\ \text{m/s}##

Speed ##= \dfrac{150}{2} = 75\ \text{km/h}##. Converting: ##75 \times \dfrac{5}{18} = \dfrac{375}{18} \approx 20.83\ \text{m/s}##.

Q13. How many metres are there in ##0.75\ \text{km}##?

##75\ \text{m}##

##750\ \text{m}##

##7500\ \text{m}##

##7.5\ \text{m}##

##0.75 \times 1000 = 750\ \text{m}##.

Q14. Express ##2## hours ##30## minutes in hours.

##2.3\ \text{h}##

##2.5\ \text{h}##

##2.05\ \text{h}##

##3\ \text{h}##

##30## minutes ##= \dfrac{30}{60} = 0.5\ \text{h}##, so the total is ##2 + 0.5 = 2.5\ \text{h}##.

Q15. A speed of ##54\ \text{km/h}## is equal to:

##9\ \text{m/s}##

##15\ \text{m/s}##

##18\ \text{m/s}##

##27\ \text{m/s}##

##54 \times \dfrac{5}{18} = 3 \times 5 = 15\ \text{m/s}##.

Q16. A bus moves at ##15\ \text{m/s}##. What distance does it cover in ##1## minute?

##15\ \text{m}##

##900\ \text{m}##

##90\ \text{m}##

##1500\ \text{m}##

##1## minute ##= 60\ \text{s}##. Distance ##= 15 \times 60 = 900\ \text{m}##. Units are consistent (m/s and s).

Q17. Which of the following correctly converts ##1\ \text{km/h}## into m/s?

##1\ \text{km/h} = \dfrac{18}{5}\ \text{m/s}##

##1\ \text{km/h} = \dfrac{5}{18}\ \text{m/s}##

##1\ \text{km/h} = 1000\ \text{m/s}##

##1\ \text{km/h} = 3600\ \text{m/s}##

##1\ \text{km/h} = \dfrac{1000\ \text{m}}{3600\ \text{s}} = \dfrac{5}{18}\ \text{m/s} \approx 0.278\ \text{m/s}##.

Q18. A train travels at ##90\ \text{km/h}##. How far does it go in ##20## seconds?

##500\ \text{m}##

##450\ \text{m}##

##900\ \text{m}##

##250\ \text{m}##

Convert speed first: ##90 \times \dfrac{5}{18} = 25\ \text{m/s}##. Distance ##= 25 \times 20 = 500\ \text{m}##.

Q19. Convert ##7200## seconds into hours.

##1\ \text{h}##

##2\ \text{h}##

##1.2\ \text{h}##

##0.5\ \text{h}##

Divide by ##3600##: ##7200 \div 3600 = 2\ \text{h}##.

Q20. A student divides a distance of ##3\ \text{km}## by a time of ##30## minutes without converting units. What is the main error?

There is no error; the answer is in km/h

The units are inconsistent, so the result is not a valid speed

Distance should always be in cm

Time cannot be divided

##3\ \text{km}## and ##30## minutes are in different unit systems. Converting ##30## minutes to ##0.5\ \text{h}## gives ##\dfrac{3}{0.5} = 6\ \text{km/h}##. Without conversion the units are inconsistent and the result is invalid.