Exam Preparation | Class 7 Science

Motion Class 7: Important Numericals with Solutions

Master speed, distance, time, average speed, unit conversion, uniform motion and pendulum numericals through simple, step-by-step solutions.

15 Solved Numericals Formula Revision Interactive Calculator Practice Quiz

Photo by Jorge Alberto Vega Barrera on Unsplash

15 Solved questions

5 Core formulas

2 Interactive tools

5 Quiz questions

What You Need to Understand First

Motion occurs when the position of an object changes with time. To solve Class 7 motion numericals, you mainly need the quantities distance, time and speed.

Important exam rule: Before substituting values in a formula, convert all distances and times into compatible units. For example, use metres with seconds or kilometres with hours.

Important Motion Formulas for Class 7

Learn these relations and identify which quantity is missing in the question.

Speed Speed = Distance / Time

Distance Distance = Speed x Time

Time Time = Distance / Speed

Average Speed Total Distance / Total Time

Time Period Total Time / Oscillations

Basic SI Unit metre per second or m/s

Length conversion: 1 kilometre = 1000 metres

Time conversion: 1 hour = 60 minutes = 3600 seconds

Speed conversion: 1 m/s = 3.6 km/h

Speed conversion: 1 km/h = 5/18 m/s

Five-Step Method for Every Numerical

1 Write the given values

2 Convert the units

3 Select the formula

4 Substitute carefully

5 Write the final unit

Interactive Motion Calculator

Use these tools to check your calculations after solving a question yourself.

Speed, Distance and Time Calculator

This calculator uses metres, seconds and metres per second.

Choose the quantity to calculate

Distance in metres

Time in seconds

Your answer will appear here.

Speed Unit Converter

Convert a speed between kilometres per hour and metres per second.

Choose conversion

Enter the speed

Your converted speed will appear here.

15 Important Motion Numericals with Solutions

Try each numerical independently before opening its solution.

Set A: Foundation Numericals Basic

1 A runner covers 180 metres in 15 seconds. Find the speed in m/s and km/h.

Given: Distance = 180 m and time = 15 s

Formula: Speed = Distance / Time

Speed = 180 / 15 Speed = 12 m/s Speed in km/h = 12 x 3.6 Speed = 43.2 km/h

Answer: The runner's speed is 12 m/s or 43.2 km/h.

2 A cyclist travels 7.2 kilometres in 30 minutes. Calculate the speed in m/s.

Given: Distance = 7.2 km and time = 30 min

Unit conversion:

7.2 km = 7.2 x 1000 = 7200 m 30 min = 30 x 60 = 1800 s

Formula: Speed = Distance / Time

Speed = 7200 / 1800 Speed = 4 m/s

Answer: The cyclist's speed is 4 m/s.

3 A child moves at a speed of 6 m/s for 8 minutes. Find the distance covered.

Given: Speed = 6 m/s and time = 8 min

Unit conversion:

8 min = 8 x 60 = 480 s

Formula: Distance = Speed x Time

Distance = 6 x 480 Distance = 2880 m Distance = 2880 / 1000 = 2.88 km

Answer: The child covers 2880 m or 2.88 km.

4 A bus covers 150 kilometres at a constant speed of 50 km/h. Find the time taken.

Given: Distance = 150 km and speed = 50 km/h

Formula: Time = Distance / Speed

Time = 150 / 50 Time = 3 h

Answer: The bus takes 3 hours.

5 A pendulum completes 45 oscillations in 72 seconds. Calculate its time period.

Given: Total time = 72 s and number of oscillations = 45

Formula: Time period = Total time / Number of oscillations

Time period = 72 / 45 Time period = 1.6 s

Answer: The time period of the pendulum is 1.6 seconds.

Set B: Conversion and Comparison Intermediate

6 Convert a speed of 54 km/h into m/s.

Rule: To convert km/h into m/s, multiply by 5/18.

Speed = 54 x 5/18 Speed = 3 x 5 Speed = 15 m/s

Answer: 54 km/h is equal to 15 m/s.

7 Convert a speed of 12 m/s into km/h.

Rule: To convert m/s into km/h, multiply by 18/5.

Speed = 12 x 18/5 Speed = 216/5 Speed = 43.2 km/h

Answer: 12 m/s is equal to 43.2 km/h.

8 Runner A completes 300 metres in 40 seconds. Runner B completes the same distance in 36 seconds. Who is faster and by how much?

Speed of Runner A:

Speed A = 300 / 40 Speed A = 7.5 m/s

Speed of Runner B:

Speed B = 300 / 36 Speed B = 8.33 m/s approximately

Difference:

Difference = 8.33 - 7.5 Difference = 0.83 m/s approximately

Answer: Runner B is faster by approximately 0.83 m/s.

9 A car's odometer changes from 24510.5 km to 24528.5 km in 24 minutes. Find the car's average speed in km/h.

Distance travelled:

Distance = 24528.5 - 24510.5 Distance = 18 km

Convert time into hours:

Time = 24/60 h Time = 0.4 h

Formula: Average speed = Total distance / Total time

Average speed = 18 / 0.4 Average speed = 45 km/h

Answer: The car's average speed is 45 km/h.

10 A car moves at 36 km/h for 20 minutes and then at 54 km/h for 30 minutes. Find the total distance and average speed.

Distance during the first part:

20 min = 20/60 h = 1/3 h Distance 1 = 36 x 1/3 Distance 1 = 12 km

Distance during the second part:

30 min = 30/60 h = 1/2 h Distance 2 = 54 x 1/2 Distance 2 = 27 km

Total distance:

Total distance = 12 + 27 Total distance = 39 km

Total time:

Total time = 20 + 30 = 50 min Total time = 50/60 h = 5/6 h

Average speed:

Average speed = 39 / (5/6) Average speed = 39 x 6/5 Average speed = 46.8 km/h

Answer: Total distance = 39 km and average speed = 46.8 km/h.

Set C: Higher-Order Numericals Exam Level

11 A car covers 60 km in the first hour, 75 km in the second hour and 45 km in the third hour. Is its motion uniform? Find its average speed.

The car covers different distances in equal intervals of one hour. Therefore, its motion is non-uniform.

Total distance = 60 + 75 + 45 Total distance = 180 km Total time = 3 h Average speed = 180 / 3 Average speed = 60 km/h

Answer: The motion is non-uniform and the average speed is 60 km/h.

12 A vehicle must cover 2 km in 200 seconds. It covers the first 500 m at 10 m/s and the next 500 m at 5 m/s. Find the speed required for the remaining distance and the average speed for the complete journey.

Time taken for the first 500 m:

Time 1 = 500 / 10 Time 1 = 50 s

Time taken for the next 500 m:

Time 2 = 500 / 5 Time 2 = 100 s

Remaining distance and time:

Total distance = 2 km = 2000 m Distance already covered = 500 + 500 = 1000 m Remaining distance = 2000 - 1000 = 1000 m Time already used = 50 + 100 = 150 s Remaining time = 200 - 150 = 50 s

Required speed:

Required speed = 1000 / 50 Required speed = 20 m/s

Average speed for the journey:

Average speed = 2000 / 200 Average speed = 10 m/s

Answer: Required speed = 20 m/s and average speed = 10 m/s.

13 An object moves uniformly and covers 8 metres every 10 seconds. Complete the missing values in the table.

Time in seconds	0	10	20	30	40	50	60	70
Distance in metres	0	8	16	24	32	40	48	56

The object covers 8 m in every interval of 10 s. Therefore, the distance increases by 8 m after every 10 s.

Distance at 20 s = 16 m Time for 32 m = 40 s Distance at 60 s = 48 m

Answer: The missing values are 16 m, 40 s and 48 m.

14 An object has travelled 60 metres after 100 seconds. Its distances recorded after every 10 seconds are 0, 6, 10, 16, 21, 29, 35, 42, 45, 55 and 60 metres. Determine the type of motion and average speed.

The increases in distance are not equal in each 10-second interval. Therefore, the speed changes and the motion is non-uniform.

Formula: Average speed = Total distance / Total time

Average speed = 60 / 100 Average speed = 0.6 m/s

Answer: The motion is non-uniform and the average speed is 0.6 m/s.

15 A train moves at 25 m/s and covers a distance of 360 km. Calculate the time taken in seconds and hours.

Given: Speed = 25 m/s and distance = 360 km

Convert the distance:

360 km = 360 x 1000 360 km = 360000 m

Formula: Time = Distance / Speed

Time = 360000 / 25 Time = 14400 s Time in hours = 14400 / 3600 Time = 4 h

Answer: The train takes 14400 seconds or 4 hours.

One-Minute Exam Challenge

A cyclist covers 1.5 km in 5 minutes. Calculate the speed in m/s and km/h.

Open the challenge solution

1.5 km = 1500 m 5 min = 300 s Speed = 1500 / 300 Speed = 5 m/s Speed in km/h = 5 x 3.6 Speed = 18 km/h

Answer: The cyclist's speed is 5 m/s or 18 km/h.

Common Mistakes to Avoid

Mixing kilometres and metres Convert the distance before using a speed expressed in m/s.

Mixing minutes and seconds Multiply minutes by 60 when the speed is given in m/s.

Using an ordinary mean for average speed Use total distance divided by total time.

Forgetting the final unit Always write m/s, km/h, metres, kilometres, seconds or hours.

Confusing an odometer with a speedometer An odometer records distance, while a speedometer displays speed.

Calling changing speed uniform motion Uniform linear motion requires equal distances in equal time intervals.

Frequently Asked Questions

What is the formula for speed in Class 7?

Speed is calculated by dividing the distance travelled by the time taken. Therefore, Speed = Distance / Time.

What is the SI unit of speed?

The SI unit of speed is metre per second, written as m/s.

How do we convert km/h into m/s?

Multiply the speed in km/h by 5/18. For example, 72 km/h multiplied by 5/18 gives 20 m/s.

What is the difference between uniform and non-uniform motion?

In uniform linear motion, an object covers equal distances in equal intervals of time. In non-uniform linear motion, its speed changes, so it covers unequal distances in equal intervals of time.

How is average speed calculated?

Average speed is calculated by dividing the total distance travelled by the total time taken for the complete journey.

How do we calculate the time period of a pendulum?

Divide the total time taken by the total number of complete oscillations. The time period is measured in seconds.

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Motion Class 7: 15 Important Numericals with Solutions