ICSE Class 8 Maths Chapter 08 Speed Distance and Time

Chapter 8

Speed, Distance And Time

8.1 Review

1. Speed

The distance covered by an object, in unit time, is called its speed.

e.g., If the speed of a car is 65 km/hr this means, the car covers a distance of 65 kilometre in one hour.

Conversely, if an object covers a distance of 20 cm in one second, its speed = 20 cm/sec.

Speed = \(\frac{\text{Distance}}{\text{Time}}\)

2. From the formula, Speed = Distance/Time we can deduce:

(i) Distance = Speed \(\times\) Time and (ii) Time = \(\frac{\text{Distance}}{\text{Speed}}\)

3. Units

Relations between the units of distance covered, speed and time are:

8.2 An Important Result

Since, 1 km/hr = \(\frac{1000 \text{ m}}{1 \text{ hr}} = \frac{1000 \text{ m}}{60 \times 60 \text{ sec}} = \frac{5}{18}\) m/s

Therefore, to convert speed from km/hr to m/s; multiply by \(\frac{5}{18}\).

Conversely, to convert speed from m/s to km/hr, multiply by \(\frac{18}{5}\).

Example 1

An aeroplane flies 450 km in 20 minutes. Find:

(i) its speed in km/hr.

(ii) time taken by it to cover 1800 km.

(iii) distance covered by it in 0.6 hours.

Solution

(i) Since, distance = 450 km and time = 20 min = \(\frac{20}{60}\) hr = \(\frac{1}{3}\) hr

Speed = \(\frac{\text{Distance}}{\text{Time}} = \frac{450 \text{ km}}{\frac{1}{3} \text{ hr}} = 1350\) km/hr

(ii) Time taken to cover 1800 km

= \(\frac{\text{Distance}}{\text{Speed}} = \frac{1800}{1350}\) hr = \(\frac{4}{3}\) hr = 1 hr 20 minutes

(iii) Distance covered in 0.6 hours = Speed \(\times\) Time = 1350 km/hr \(\times\) 0.6 hr = 810 km

Teacher's Note

Understanding speed helps us plan our travel time for daily activities - whether catching a bus to school or planning a road trip with family.

1. Uniform speed

If an object covers equal distances in equal intervals of time, its speed is said to be uniform.

2. Variable speed

When the speed of a body is not uniform, it is variable.

i.e. if an object covers unequal distances in equal intervals of time, its speed is variable.

Unless mentioned, the speed is always taken as uniform.

3. Average speed

Usually, a moving object (car, motor-cycle, etc.) does not cover its entire distance with the same (uniform) speed. Sometimes it increases its speed, sometimes it reduces its speed and sometimes it stops also.

Under such circumstances, the total distance covered by the moving object divided by the time, taken by it to cover this distance, gives the average speed of the object.

Average speed = \(\frac{\text{Total distance travelled}}{\text{Total time taken}}\)

Example 2

A man covers a distance of 60 km at a speed of 40 km/hr and another distance of 50 km at a speed of 30 km/hr. Calculate his average speed for the whole journey.

Solution

(i) Time taken to cover 60 km = \(\frac{60}{40}\) hrs = \(\frac{3}{2}\) hrs

and, time taken to cover 50 km = \(\frac{50}{30}\) hrs = \(\frac{5}{3}\) hrs

Total distance travelled = 60 km + 50 km = 110 km

and, total time taken = \(\frac{3}{2}\) hrs + \(\frac{5}{3}\) hrs = \(\frac{9 + 10}{6}\) hrs = \(\frac{19}{6}\) hrs

Average speed = \(\frac{\text{Total distance travelled}}{\text{Total time taken}}\)

= \(\frac{110 \text{ km}}{\frac{19}{6} \text{ hrs}} = \frac{110 \times 6}{19}\) km/hr = \(34\frac{14}{19}\) km/hr

Example 3

A distance of 450 km is covered in \(6\frac{1}{2}\) hrs. If the first two-thirds of the distance is covered at the speed of 75 km/hr, at what speed the remaining distance is covered?

Solution

Since, two-thirds of the whole distance = \(\frac{2}{3} \times 450\) km = 300 km

And, the speed with which this distance is covered = 75 km/hr

Therefore, the time taken to cover this distance = \(\frac{\text{Distance}}{\text{Speed}} = \frac{300}{75}\) hrs = 4 hrs

For the remaining distance:

Distance to be covered = (450 - 300) km = 150 km

and, time taken = \((6\frac{1}{2} - 4)\) hrs = \(2\frac{1}{2}\) hrs = \(\frac{5}{2}\) hrs

Speed = \(\frac{150 \text{ km}}{\frac{5}{2} \text{ hrs}} = 60\) km/hr

Teacher's Note

Real-world journeys rarely maintain one speed - calculating average speed helps us understand how traffic delays and different road conditions affect our total travel time in daily commutes.