36 practice questions on speed-and-its-calculation from the Measurement of Time and Motion section of the UPSC Prelims syllabus. 36 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.
A boy runs at a steady $5\ \text{m/s}$. The time he takes to cover $100\ \text{m}$ is
Correct answer: D - $20\ \text{s}$
Dividing distance by speed gives $100 \div 5 = 20\ \text{s}$. The value $5$ is the speed itself, $95$ is the difference of the two numbers, and $500$ comes from multiplying instead of dividing.
If two objects travel for the same length of time, the one with the greater speed
Correct answer: C - covers a greater distance
Speed is the distance covered in each unit of time, so over an equal time the faster object gets further. Covering less ground would mean it was the slower one, and equal distances would mean equal speeds. The times were fixed as equal at the start, so neither can take longer.
A boy walks $1.2\ \text{km}$ to school at a steady $1\ \text{m/s}$. The time he takes is
Correct answer: A - $20\ \text{min}$
The distance is $1200\ \text{m}$ and the speed is $1\ \text{m/s}$, so the walk takes $1200\ \text{s}$, which is $20\ \text{min}$. The values $12$ and $1.2$ come from using the kilometre figure without converting, and $72$ would need a speed far below $1\ \text{m/s}$.
A student walks $3\ \text{km}$ to school at $3\ \text{km/h}$ and returns along the same road at $6\ \text{km/h}$. The average speed for the whole trip is
Correct answer: A - $4\ \text{km/h}$
Going takes $3 \div 3 = 1$ hour and returning takes $3 \div 6 = 0.5$ hours, so the student covers $6\ \text{km}$ in $1.5$ hours, giving $6 \div 1.5 = 4\ \text{km/h}$. Averaging the two speeds gives $4.5$, which is wrong because more time is spent at the slower speed. The values $3$ and $9$ come from using one leg only or from adding the speeds.
The average speed of a journey is found by dividing
Correct answer: A - the total distance by the total time
Average speed describes the whole journey as if it had been covered steadily, so it is the total distance divided by the total time taken. Dividing the other way round gives a time per unit distance. Comparing the highest and lowest speeds or counting stops tells us nothing about the average.
A bus covers $2.4\ \text{km}$ in $4$ minutes. Its speed in metres per second is
Correct answer: C - $10\ \text{m/s}$
Changing both quantities to SI units gives $2400\ \text{m}$ and $240\ \text{s}$, so the speed is $2400 \div 240 = 10\ \text{m/s}$. Dividing $2.4$ by $4$ gives $0.6$, forgetting to change minutes to seconds gives $600$, and $36$ is the speed in $\text{km/h}$ rather than in $\text{m/s}$.
A cyclist covers $9\ \text{km}$ in $30$ minutes. The speed of the cyclist is
Correct answer: B - $18\ \text{km/h}$
Thirty minutes is half an hour, so the speed is $9 \div 0.5 = 18\ \text{km/h}$. Halving instead of doubling gives $4.5$, ignoring the time gives $9$, and dividing kilometres by minutes without converting gives the meaningless $300$.
A train travels at a steady $90\ \text{km/h}$. The time it takes to cover $45\ \text{km}$ is
Correct answer: D - $30\ \text{min}$
The time is $45 \div 90 = 0.5$ hours, which is $30\ \text{min}$. Reading the distance as the answer gives $45\ \text{min}$, dividing $90$ by $45$ gives $2$, and $120\ \text{min}$ would be two full hours.
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