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Motion - Speed and Average Speed

Grade 7ICSE

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

🔑Concepts

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Speed is defined as the distance traveled by an object per unit time. It indicates how fast an object is moving.

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Speed is a scalar quantity because it has magnitude but no specific direction.

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The S.I. unit of speed is meters per second (m/sm/s or ms−1ms^{-1}), while the C.G.S. unit is centimeters per second (cm/scm/s). For long distances, kilometers per hour (km/hkm/h) is commonly used.

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Uniform Speed: An object is said to be moving with uniform speed if it covers equal distances in equal intervals of time, however small these intervals may be.

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Non-uniform (Variable) Speed: An object is said to be moving with non-uniform speed if it covers unequal distances in equal intervals of time.

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Average Speed: For an object moving with variable speed, average speed is the total distance traveled divided by the total time taken to cover that distance.

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

📐Formulae

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

Average Speed=Total Distance TraveledTotal Time TakenAverage\ Speed = \frac{Total\ Distance\ Traveled}{Total\ Time\ Taken}

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

Distance=Speed×TimeDistance = Speed \times Time

💡Examples

Problem 1:

A car travels a distance of 200 km200\ km in 4 hours4\ hours. Calculate its speed in km/hkm/h and m/sm/s.

Solution:

Speed in km/h=200 km4 h=50 km/hkm/h = \frac{200\ km}{4\ h} = 50\ km/h. To convert to m/sm/s: 50×518=25018≈13.89 m/s50 \times \frac{5}{18} = \frac{250}{18} \approx 13.89\ m/s.

Explanation:

First, we use the basic formula for speed. Then, we apply the conversion factor 518\frac{5}{18} to change the units from km/hkm/h to m/sm/s.

Problem 2:

A train travels the first 60 km60\ km at a speed of 40 km/h40\ km/h and the next 60 km60\ km at a speed of 60 km/h60\ km/h. Find the average speed of the train.

Solution:

Time for first part t1=6040=1.5 ht_1 = \frac{60}{40} = 1.5\ h. Time for second part t2=6060=1 ht_2 = \frac{60}{60} = 1\ h. Total distance = 60+60=120 km60 + 60 = 120\ km. Total time = 1.5+1=2.5 h1.5 + 1 = 2.5\ h. Average speed = 1202.5=48 km/h\frac{120}{2.5} = 48\ km/h.

Explanation:

Average speed is NOT the mean of the two speeds. We must calculate the total time taken for the entire journey and divide the total distance by that total time.