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Motion and Time - Units of Time and Speed

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Speed is defined as the distance covered by an object in a unit of time. It determines how fast or slow an object is moving.

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The basic unit of time is the second (ss). Other larger units include minutes (minmin) and hours (hh).

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The basic unit of speed is metre per second (m/sm/s). It can also be expressed in other units such as km/hkm/h or cm/scm/s.

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A simple pendulum is used to measure time. The time taken by the pendulum to complete one oscillation is called its Time Period (TT).

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To convert speed from km/hkm/h to m/sm/s, we multiply the value by 518\frac{5}{18}. To convert m/sm/s to km/hkm/h, we multiply by 185\frac{18}{5}.

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A speedometer records the speed of a vehicle directly in km/hkm/h, while an odometer measures the total distance moved by the vehicle.

📐Formulae

Speed=Total Distance coveredTotal Time takenSpeed = \frac{\text{Total Distance covered}}{\text{Total Time taken}}

Distance=Speed×TimeDistance = Speed \times Time

Time=DistanceSpeedTime = \frac{Distance}{Speed}

Time Period(T)=Total TimeNumber of Oscillations\text{Time Period} (T) = \frac{\text{Total Time}}{\text{Number of Oscillations}}

1 km/h=1000 m3600 s=518 m/s1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s}

💡Examples

Problem 1:

A car covers a distance of 180 km180 \text{ km} in 3 hours3 \text{ hours}. Calculate its speed in km/hkm/h and m/sm/s.

Solution:

Given: Distance=180 kmDistance = 180 \text{ km}, Time=3 hTime = 3 \text{ h}. Speed in km/h=180 km3 h=60 km/hkm/h = \frac{180 \text{ km}}{3 \text{ h}} = 60 \text{ km/h}. To convert to m/sm/s: 60×518≈16.67 m/s60 \times \frac{5}{18} \approx 16.67 \text{ m/s}.

Explanation:

We use the formula Speed=DistanceTimeSpeed = \frac{Distance}{Time} for the initial calculation and then apply the conversion factor 518\frac{5}{18} to find the speed in SI units.

Problem 2:

A simple pendulum takes 32 s32 \text{ s} to complete 2020 oscillations. What is the time period of the pendulum?

Solution:

Number of oscillations = 2020. Total time taken = 32 s32 \text{ s}. Time Period(T)=32 s20=1.6 s\text{Time Period} (T) = \frac{32 \text{ s}}{20} = 1.6 \text{ s}.

Explanation:

The time period is the time taken for one single oscillation, calculated by dividing the total time by the total number of oscillations.

Problem 3:

If a train moves at a speed of 90 km/h90 \text{ km/h}, how much distance will it cover in 15 minutes15 \text{ minutes}?

Solution:

Speed = 90 km/h90 \text{ km/h}. Time = 15 min=1560 h=0.25 h15 \text{ min} = \frac{15}{60} \text{ h} = 0.25 \text{ h}. Distance=Speed×Time=90 km/h×0.25 h=22.5 kmDistance = Speed \times Time = 90 \text{ km/h} \times 0.25 \text{ h} = 22.5 \text{ km}.

Explanation:

First, convert the time from minutes to hours to ensure the units match the speed (km/hkm/h), then multiply speed by time to find distance.