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Measurement of Time and Motion - Uniform and Non-uniform Linear Motion

Grade 7CBSE

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

🔑Concepts

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Motion is the change in position of an object with respect to time.

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Speed is defined as the total distance covered divided by the total time taken. The SI unit of speed is m/sm/s, though km/hkm/h is also commonly used.

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Uniform Motion: An object moving along a straight line is said to be in uniform motion if its speed remains constant over time. It covers equal distances in equal intervals of time.

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Non-uniform Motion: If the speed of an object moving along a straight line keeps changing, its motion is said to be non-uniform motion. It covers unequal distances in equal intervals of time.

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Distance-Time Graph: For uniform motion, the distance-time graph is a straight line passing through the origin. For non-uniform motion, the graph is a curved line.

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Average Speed: It is the total distance travelled by an object divided by the total time taken: Average Speed=Total DistanceTotal Time Taken\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time Taken}}.

📐Formulae

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

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

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

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

1 m/s=185 km/h1 \text{ m/s} = \frac{18}{5} \text{ km/h}

💡Examples

Problem 1:

A car travels a distance of 150 km150 \text{ km} in 3 hours3 \text{ hours}. Calculate its speed in km/hkm/h.

Solution:

Speed=150 km3 h=50 km/hSpeed = \frac{150 \text{ km}}{3 \text{ h}} = 50 \text{ km/h}

Explanation:

To find the speed, we divide the total distance (150 km150 \text{ km}) by the total time (3 h3 \text{ h}). The resulting speed is 50 km/h50 \text{ km/h}.

Problem 2:

Determine the distance covered by a bus moving at a constant speed of 20 m/s20 \text{ m/s} for 50 seconds50 \text{ seconds}.

Solution:

Distance=20 m/s×50 s=1000 m\text{Distance} = 20 \text{ m/s} \times 50 \text{ s} = 1000 \text{ m}

Explanation:

Distance is the product of speed and time. Since the speed is 20 m/s20 \text{ m/s} and time is 50 s50 \text{ s}, the distance is 1000 m1000 \text{ m} or 1 km1 \text{ km}.

Problem 3:

An odometer of a car reads 57321 km57321 \text{ km} at 08:30 AM08:30 \text{ AM} and 57336 km57336 \text{ km} at 08:50 AM08:50 \text{ AM}. Calculate the distance moved by the car.

Solution:

57336−5732115\begin{array}{r} 57336 \\ - 57321 \\ \hline 15 \end{array} Therefore, Distance=15 km\text{Distance} = 15 \text{ km}.

Explanation:

The distance moved is the difference between the final odometer reading and the initial odometer reading. Subtracting 5732157321 from 5733657336 gives 15 km15 \text{ km}.

Problem 4:

A train covers 30 km30 \text{ km} in the first hour and 45 km45 \text{ km} in the second hour. Is the motion uniform or non-uniform?

Solution:

Speed1=30 km1 h=30 km/h\text{Speed}_1 = \frac{30 \text{ km}}{1 \text{ h}} = 30 \text{ km/h} Speed2=45 km1 h=45 km/h\text{Speed}_2 = \frac{45 \text{ km}}{1 \text{ h}} = 45 \text{ km/h}

Explanation:

Since the train covers unequal distances (30 km30 \text{ km} and 45 km45 \text{ km}) in equal intervals of time (1 hour1 \text{ hour} each), the speed is not constant. Therefore, the motion is non-uniform.