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Measurement of Time and Motion - 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 time. It is a measure of how fast an object moves. The basic unit of speed is m/sm/s, though km/hkm/h is also commonly used.

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Motion can be classified into two types: Uniform Motion and Non-uniform Motion. In Uniform Motion, an object moves along a straight line with a constant speed. In Non-uniform Motion, the speed of an object moving along a straight line keeps changing.

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Average Speed is the total distance covered divided by the total time taken. For most real-world scenarios where speed fluctuates, we use the formula: Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}.

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A Speedometer is a device used in vehicles to measure the speed of the vehicle in km/hkm/h at that particular instant.

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An Odometer is an instrument used to measure the total distance traveled by a vehicle.

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Time measurement in ancient times relied on periodic events like the sun rising or the moon's phases. Modern time measurement is based on periodic motion, such as the simple pendulum.

📐Formulae

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

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 travels a distance of 250 km250 \text{ km} in 5 hours5 \text{ hours}. Calculate its speed.

Solution:

Given: Distance=250 km\text{Distance} = 250 \text{ km}, Time=5 hours\text{Time} = 5 \text{ hours}. Using the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}, we get Speed=2505=50 km/h\text{Speed} = \frac{250}{5} = 50 \text{ km/h}.

Explanation:

To find the speed, we divide the total distance by the total time taken.

Problem 2:

Calculate the total distance covered by a cyclist who travels at a speed of 12 km/h12 \text{ km/h} for 3 hours3 \text{ hours} and then 15 km/h15 \text{ km/h} for 2 hours2 \text{ hours}.

Solution:

Distance 1: 12×3=36 km12 \times 3 = 36 \text{ km}. Distance 2: 15×2=30 km15 \times 2 = 30 \text{ km}. Total Distance: 36+30=66 km36 + 30 = 66 \text{ km}.

36+3066\begin{array}{r} 36 \\ + 30 \\ \hline 66 \end{array}

Explanation:

First, calculate the distance for each segment using Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}, then add the results to find the total distance.

Problem 3:

Convert the speed of 72 km/h72 \text{ km/h} into m/sm/s.

Solution:

72 km/h=72×518 m/s72 \text{ km/h} = 72 \times \frac{5}{18} \text{ m/s} =4×5=20 m/s= 4 \times 5 = 20 \text{ m/s}

Explanation:

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