Measurement of Length and Motion – Numerical Problems with Stepwise Solutions
CBSE Class 6 Science — Chapter 5: Measurement of Length and Motion
20 Numerical Problems with stepwise solutions — NCERT-aligned for CBSE Class 6 examinations.
Content Bank — Important formulas & conversions
- Unit conversions:
1 m = 100 cm,1 m = 1000 mm,1 km = 1000 m. - Speed formula:
speed = distance / time(v = d / t). - Average speed:
average speed = total distance / total time. - Time conversions:
1 min = 60 s,1 h = 60 min = 3600 s. - Trundle wheel: distance =
number of turns × circumference. - Always keep units consistent when calculating (convert km↔m or min↔h as needed).
20 Numerical Problems — Topic-wise with Stepwise Solutions
Each problem includes clear steps and final answer with correct units.
Problem 1: Convert 2.75 metres into centimetres and millimetres.
Solution:
- 1 m = 100 cm ⇒ 2.75 m = 2.75 × 100 = 275 cm.
- 1 m = 1000 mm ⇒ 2.75 m = 2.75 × 1000 = 2750 mm.
Problem 2: Express 4500 m in kilometres.
- 1 km = 1000 m. So 4500 m = 4500 ÷ 1000 = 4.5 km.
Problem 3: A ribbon is 123 cm long. Express its length in metres (to two decimal places).
- 1 m = 100 cm. So length in m = 123 ÷ 100 = 1.23 m.
- Answer: 1.23 m.
Problem 4: A toy train track is 2.2 m long. How many millimetres long is it?
- 1 m = 1000 mm. So 2.2 m = 2.2 × 1000 = 2200 mm.
Problem 5: A student measures a rope using a metre scale by marking three segments: 0.9 m, 0.8 m and 0.75 m. What is the total length of the rope in metres and in centimetres?
- Total (m) = 0.9 + 0.8 + 0.75 = 2.45 m.
- Convert to cm: 2.45 × 100 = 245 cm.
Problem 6: A measuring wheel with circumference 0.5 m makes 26 full turns. What distance did it record?
- Distance = turns × circumference = 26 × 0.5 = 13 m.
Problem 7: In an experiment a student times a toy car for three trials: 2.4 s, 2.6 s and 2.5 s. The car covers 6 m each trial. Calculate the average time and average speed (in m/s).
- Average time = (2.4 + 2.6 + 2.5) ÷ 3 = 7.5 ÷ 3 = 2.5 s.
- Distance = 6 m. Average speed = distance / average time = 6 ÷ 2.5 = 2.4 m/s.
Problem 8: A student traces a curved path on paper with a thread and finds the thread length to be 24 cm. If the map scale is 1 cm : 2 km, what is the real distance?
- Map length = 24 cm. Scale: 1 cm = 2 km ⇒ real distance = 24 × 2 = 48 km.
Problem 9: A cyclist travels 12 km in 0.5 hour. Find the speed in km/h and in m/s.
- Speed (km/h) = 12 ÷ 0.5 = 24 km/h.
- To convert to m/s: 1 km/h = 1000/3600 m/s = 1/3.6 m/s. So 24 ÷ 3.6 = 6.67 m/s (approx).
Problem 10: A runner covers 400 m in 50 s. What is the speed in m/s and km/h (rounded to two decimals)?
- Speed (m/s) = 400 ÷ 50 = 8 m/s.
- Speed (km/h) = 8 × 3.6 = 28.80 km/h.
Problem 11: A car moves 90 km in 1.5 hours. Find its speed in km/h and in m/s.
- Speed (km/h) = 90 ÷ 1.5 = 60 km/h.
- Convert to m/s: 60 ÷ 3.6 = 16.67 m/s (approx).
Problem 12: A toy car moves 15 m in 3 s and then 25 m in 5 s. What is the average speed for the whole trip in m/s?
- Total distance = 15 + 25 = 40 m. Total time = 3 + 5 = 8 s.
- Average speed = 40 ÷ 8 = 5 m/s.
Problem 13: Convert 150 seconds into minutes and seconds.
- 150 s = 150 ÷ 60 = 2 minutes remainder 30 seconds ⇒ 2 min 30 s.
Problem 14: A walker covers 3 km in 45 minutes. What is the speed in km/h and in m/s?
- Convert 45 min to hours: 45 ÷ 60 = 0.75 h.
- Speed (km/h) = 3 ÷ 0.75 = 4 km/h.
- Convert to m/s: 4 ÷ 3.6 = 1.11 m/s (approx).
Problem 15: A car travels 360 km in 4 hours 30 minutes. Find the average speed in km/h.
- Convert time to hours: 4 h 30 min = 4 + 30/60 = 4.5 h.
- Speed = 360 ÷ 4.5 = 80 km/h.
Problem 16: A magnet picks up 18 iron pins in one stroke. If a student performs 7 strokes, how many pins will be picked up in total (assuming unlimited pins)?
- Pins per stroke = 18. Number of strokes = 7. Total = 18 × 7 = 126 pins.
Problem 17: A meter-long stick is cut into 8 equal pieces. What is the length of each piece in cm and mm?
- 1 m = 100 cm. Each piece = 100 ÷ 8 = 12.5 cm = 12.5 cm.
- In mm: 12.5 cm = 125 mm.
Problem 18: After an experiment, a magnet can pick 40 pins. After gentle hammering its capacity falls by 25%. How many pins can it now pick?
- Loss = 25% of 40 = 0.25 × 40 = 10 pins.
- Remaining = 40 − 10 = 30 pins.
Problem 19: A student measures three lengths: 12.3 cm, 12.5 cm and 12.4 cm. Find the average length.
- Total = 12.3 + 12.5 + 12.4 = 37.2 cm.
- Average = 37.2 ÷ 3 = 12.4 cm.
Problem 20: A toy car takes 0.8 s to travel 2 m. If the same car travelled 10 m at the same speed, how long would it take?
- Speed = distance / time = 2 ÷ 0.8 = 2.5 m/s.
- Time for 10 m = distance / speed = 10 ÷ 2.5 = 4 s.