Measurement of Time and Motion – Numerical Problems with Stepwise Solutions
CBSE Class 7 Science — Chapter 8: Measurement of Time & Motion
Topic-wise set of 20 numerical problems with clear, step-by-step solutions — strictly aligned with NCERT for Class 7 (CBSE standard).
Content Bank — Important Formulas (Chapter 8)
Speed (average)
speed = \frac{distance}{time}Units: m/s, km/hDistance
distance = speed \times timeTime
time = \frac{distance}{speed}Unit conversions
1 km = 1000 m; 1 h = 3600 s; 1 m/s = 3.6 km/hTopic: Basic Speed & Time Calculations
Problem 1
Rahul walks 3 km in 30 minutes. Calculate his average speed in km/h and m/s.
Show stepwise solution
Step 1: Convert time to hours: 30 minutes = 0.5 hour.
Step 2: Average speed (km/h) = distance / time = 3 km / 0.5 h = 6 km/h.
Step 3: To convert to m/s, use 1 km/h = (1000 m)/(3600 s) = 1/3.6 m/s. So 6 km/h = 6 ÷ 3.6 = 1.666... m/s ≈ 1.67 m/s.
Answer: 6 km/h (≈ 1.67 m/s).
Problem 2
A car covers 150 km in 2.5 hours. Find its average speed in km/h and in m/s.
Show stepwise solution
Step 1: Average speed (km/h) = 150 km / 2.5 h = 60 km/h.
Step 2: Convert to m/s: 60 ÷ 3.6 = 16.666... m/s ≈ 16.67 m/s.
Answer: 60 km/h (≈ 16.67 m/s).
Problem 3
A cyclist covers 20 km in 50 minutes. Calculate his speed in km/h.
Show stepwise solution
Step 1: Convert 50 minutes to hours: 50/60 = 5/6 ≈ 0.8333 h.
Step 2: Speed = distance/time = 20 km / (5/6 h) = 20 × (6/5) = 24 km/h.
Answer: 24 km/h.
Topic: Distance from Speed and Time
Problem 4
A train runs at a constant speed of 72 km/h. How far will it travel in 15 minutes?
Show stepwise solution
Step 1: Convert 15 minutes to hours: 15/60 = 0.25 h.
Step 2: Distance = speed × time = 72 km/h × 0.25 h = 18 km.
Answer: 18 km.
Problem 5
A sprinter runs at 9 m/s. How far does he run in 12 seconds?
Show stepwise solution
Step 1: Use distance = speed × time = 9 m/s × 12 s = 108 m.
Answer: 108 m.
Problem 6
A bus moves at 54 km/h for 40 minutes. Find the distance covered (in km).
Show stepwise solution
Step 1: Convert 40 min to hours: 40/60 = 2/3 ≈ 0.6667 h.
Step 2: Distance = 54 × 2/3 = 36 km.
Answer: 36 km.
Topic: Relative Speed
Problem 7
Two cars move in opposite directions towards each other with speeds 50 km/h and 70 km/h. If they are 240 km apart, after how much time will they meet?
Show stepwise solution
Step 1: Relative speed (opposite directions) = 50 + 70 = 120 km/h.
Step 2: Time = distance / relative speed = 240 km / 120 km/h = 2 h.
Answer: 2 hours.
Problem 8
Two runners start at the same point and run in the same direction at speeds 8 m/s and 5 m/s. How long will it take the faster runner to be 90 m ahead?
Show stepwise solution
Step 1: Relative speed (same direction) = 8 - 5 = 3 m/s.
Step 2: Time = distance / relative speed = 90 m / 3 m/s = 30 s.
Answer: 30 seconds.
Topic: Unit Conversions & Practical Calculations
Problem 9
Convert a speed of 18 m/s to km/h.
Show stepwise solution
Step 1: 1 m/s = 3.6 km/h, so 18 m/s = 18 × 3.6 = 64.8 km/h.
Answer: 64.8 km/h.
Problem 10
A car moves at 90 km/h. Express its speed in m/s.
Show stepwise solution
Step 1: 1 km/h = 1/3.6 m/s, so 90 km/h = 90 ÷ 3.6 = 25 m/s.
Answer: 25 m/s.
Problem 11
How many seconds are there in 2.5 hours?
Show stepwise solution
Step 1: 1 hour = 3600 seconds. So 2.5 h = 2.5 × 3600 = 9000 s.
Answer: 9000 seconds.
Topic: Graphs & Conceptual Calculations
Problem 12
On a distance-time graph, a straight line from (0,0) to (2 h, 100 km) is plotted. Find the speed.
Show stepwise solution
Step 1: Speed = change in distance / change in time = 100 km / 2 h = 50 km/h.
Answer: 50 km/h.
Problem 13
A person remains at rest for 30 min and then walks 3 km in 30 min. What is his average speed for the whole 1 hour?
Show stepwise solution
Step 1: Total distance = 3 km. Total time = 1 h.
Step 2: Average speed = 3 km / 1 h = 3 km/h.
Answer: 3 km/h.
Topic: Mixed Numerical Problems
Problem 14
A car covers 360 km at a uniform speed in 6 hours. After 3 hours it has already covered 180 km. Is the motion uniform? Explain and find the speed.
Show stepwise solution
Step 1: Overall average speed = 360/6 = 60 km/h.
Step 2: In first 3 hours it covered 180 km → speed = 180/3 = 60 km/h. Since equal distances are covered in equal time intervals, motion is uniform.
Answer: Yes, motion is uniform; speed = 60 km/h.
Problem 15
An athlete completes 400 m in 50 s and then walks 100 m in 80 s. What is his average speed for the whole trip?
Show stepwise solution
Step 1: Total distance = 400 + 100 = 500 m.
Step 2: Total time = 50 + 80 = 130 s.
Step 3: Average speed = 500 m / 130 s ≈ 3.846 m/s ≈ 3.85 m/s.
Answer: ≈ 3.85 m/s.
Problem 16
A vehicle moves 30 km north and then 40 km east. What is the total distance and the magnitude of displacement from the starting point?
Show stepwise solution
Step 1: Total distance = 30 + 40 = 70 km.
Step 2: Displacement is the straight-line from start to end; use Pythagoras: sqrt(30^2 + 40^2) = sqrt(900 + 1600) = sqrt(2500) = 50 km.
Answer: Distance = 70 km; Displacement = 50 km.
Problem 17
A motorboat goes upstream at 12 km/h and downstream at 18 km/h. Find the speed of the boat in still water and the speed of the stream.
Show stepwise solution
Step 1: Let boat speed in still water = b, stream speed = s. Then downstream = b + s = 18; upstream = b - s = 12.
Step 2: Add both: (b+s) + (b-s) = 18 + 12 → 2b = 30 → b = 15 km/h.
Step 3: Now s = 18 - b = 3 km/h.
Answer: Boat speed = 15 km/h; Stream speed = 3 km/h.
Problem 18
Shreya cycles 12 km at 15 km/h and then 8 km at 10 km/h. Calculate her overall average speed.
Show stepwise solution
Step 1: Time for first part = 12 / 15 = 0.8 h.
Step 2: Time for second part = 8 / 10 = 0.8 h.
Step 3: Total distance = 20 km. Total time = 0.8 + 0.8 = 1.6 h.
Step 4: Average speed = 20 / 1.6 = 12.5 km/h.
Answer: 12.5 km/h.
Problem 19
A car takes 4 hours to travel from A to B at 60 km/h. On return, because of traffic, its speed reduces to 40 km/h. What is the average speed for the whole round trip?
Show stepwise solution
Step 1: Distance one-way = speed × time = 60 × 4 = 240 km.
Step 2: Time for return = distance / speed = 240 / 40 = 6 h.
Step 3: Total distance = 240 + 240 = 480 km. Total time = 4 + 6 = 10 h.
Step 4: Average speed = 480 / 10 = 48 km/h.
Answer: 48 km/h.
Problem 20
An object is moving so that its displacement x (in metres) from origin after t seconds is x = 5t. Find its speed and state whether the motion is uniform.
Show stepwise solution
Step 1: Displacement x = 5t means in each 1 s the object moves 5 m. So speed = change in x / change in t = 5 m/s.
Step 2: Since displacement increases by equal amounts in equal time intervals, motion is uniform.
Answer: Speed = 5 m/s; Motion is uniform.