Quiz: Fundamentals of Time, Speed, and Distance 1
This quiz accompanies Lesson 1: Introduction to Time, Speed, and Distance from the course Time, Speed & Distance: Core Concepts for Competitive Exams.
The lesson establishes the essential building blocks you will use throughout the entire course:
- Speed as the rate at which distance is covered per unit time.
- The fundamental relationship between distance, speed, and time.
- Unit consistency — why mixing km/h with minutes leads to wrong answers.
- Basic formula application and simple word problems.
All 20 questions are answerable from this lesson alone. Work carefully, watch your units, and good luck!
Q1. Speed is best defined as:
Speed measures how much distance is covered in each unit of time, i.e. distance divided by time.
Q2. Which formula correctly relates distance, speed, and time?
The fundamental relation is distance equals speed multiplied by time. The other forms are rearrangements used to find speed or time.
Q3. A car travels ##150## km in ##3## hours. Its average speed is:
Speed ##= \dfrac{\text{Distance}}{\text{Time}} = \dfrac{150}{3} = 50## km/h.
Q4. If speed is kept constant and the time of travel is doubled, the distance covered:
Since distance ##=## speed ##\times## time, doubling the time at constant speed doubles the distance.
Q5. A train covers ##240## km at a uniform speed of ##80## km/h. The time taken is:
Time ##= \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{240}{80} = 3## hours.
Q6. To convert a speed given in km/h into m/s, you should:
Since ##1## km ##= 1000## m and ##1## h ##= 3600## s, ##1## km/h ##= \dfrac{1000}{3600} = \dfrac{5}{18}## m/s.
Q7. A speed of ##72## km/h expressed in m/s is:
##72 \times \dfrac{5}{18} = 4 \times 5 = 20## m/s.
Q8. A cyclist rides at ##5## m/s for ##2## minutes. The distance covered is:
Convert time to seconds: ##2## min ##= 120## s. Distance ##= 5 \times 120 = 600## m.
Q9. Which of the following is a valid unit of speed?
Speed is distance per unit time, so km/h (kilometres per hour) is a valid unit. h/km would be a unit of time per distance.
Q10. A student computes speed as ##\dfrac{120 \text{ km}}{2 \text{ h}}## but writes the answer as ##60## m/s. The error is:
Dividing km by hours gives km/h, not m/s. The numerical answer ##60## is correct only in km/h; the unit must match the quantities used.
Q11. A bus covers ##90## km in ##1.5## hours. Its average speed is:
Speed ##= \dfrac{90}{1.5} = 60## km/h.
Q12. If distance is constant and speed is doubled, the time taken:
From time ##= \dfrac{\text{distance}}{\text{speed}}##, doubling the speed at fixed distance halves the time.
Q13. A runner covers ##400## m in ##50## seconds. His speed in km/h is:
Speed ##= \dfrac{400}{50} = 8## m/s. Converting: ##8 \times \dfrac{18}{5} = 28.8## km/h.
Q14. A car moving at ##54## km/h covers a distance in ##20## minutes. The distance is:
Convert time: ##20## min ##= \dfrac{1}{3}## h. Distance ##= 54 \times \dfrac{1}{3} = 18## km.
Q15. The relation between distance, speed, and time can be rearranged to give speed as:
Rearranging distance ##=## speed ##\times## time gives speed ##= \dfrac{\text{distance}}{\text{time}}##.
Q16. A train travels ##300## km at ##60## km/h and then ##200## km at ##50## km/h. The total time taken is:
First part: ##\dfrac{300}{60} = 5## h. Second part: ##\dfrac{200}{50} = 4## h. Total ##= 5 + 4 = 9## h.
Q17. A speed of ##10## m/s expressed in km/h is:
##10 \times \dfrac{18}{5} = 2 \times 18 = 36## km/h.
Q18. A man walks ##1.2## km in ##15## minutes. His speed in m/s is:
Distance ##= 1.2## km ##= 1200## m; time ##= 15## min ##= 900## s. Speed ##= \dfrac{1200}{900} \approx 1.33## m/s.
Q19. Two cars travel the same distance. Car A takes ##2## hours and Car B takes ##4## hours. Which statement is correct?
For the same distance, the car taking less time has the greater speed, since speed ##= \dfrac{\text{distance}}{\text{time}}##.
Q20. A vehicle covers ##45## km in ##45## minutes. Its speed in km/h is:
Convert time: ##45## min ##= 0.75## h. Speed ##= \dfrac{45}{0.75} = 60## km/h.