Speed Distance and Time

Can you tell which moves faster - a motorcycle or a bicycle? Certainly, a motorcycle, because a motorcycle can cover longer distance in shorter time. In other words, we can say, a motorcycle runs at a greater speed than a bicycle.

For knowing how fast an object moves, we consider the distance travelled by it and the time taken in travelling the distance.

The distance travelled in a unit time by an object is called its speed.

Speed is the distance covered by an object in a unit time.

Speed = $\frac{\textrm{Distance}}{\textrm{Time}}$

From the above formula, we can derive the following relationship.

Time = $\frac{\textrm{Distance}}{\textrm{Speed}}$

Distance = Time x Speed

If we represent speed by S, Distance by D and Time by T, we can express the relationship between them as follows.

S = $\frac{\textrm{D}}{\textrm{T}}$

T = $\frac{\textrm{D}}{\textrm{S}}$

D = T x S

We measure speed in kilometres per hour (km/hr) metres per minute (m/min) or metres per second (m/sec).

Suppose an Express train leaves the station A at 0900 hours. It runs nonstop and reaches the station B at 1100 hours. So the Express train take 2 hours to cover the distance. A Mail train covers the distance between these stations in 3 hours. If the distance between the two stations is 120 km, which train travels faster?

To find this, we use the unitary method.

The distance covered by the Express train in 2 hours = 120 km

The distance covered by the Express train in 1 hour = $\frac{120}{2}$ km = 60 km

The distance covered by the Mail train in 3 hours = 120 km

The distance covered by the Mail train in 1 hour = $\frac{120}{3}$ km = 40 km

So, the Express train travels more distance than the Mail train in 1 hour. Hence, the Express train travels faster than the Mail train. We say that the Express train has greater speed than the Mail train.

Speed: The distance travelled by a body or vehicle in a unit time is known as its speed.

Speed = $\frac{\textrm{Distance (in unit of length)}}{\textrm{Time (in unit of time)}}$

Average Speed: The total distance covered by a body divided by the total time taken by the body is known as average speed.

Average Speed = $\frac{\textrm{Total distance travelled}}{\textrm{Total Time Taken}}$

and Speed = $\frac{\textrm{Total Distance Covered}}{\textrm{Total time taken-time of stoppage}}$

         = $\frac{\textrm{Distance}}{\textrm{Time}}$

If there is no stoppage, that is, the time of stoppage is zero, the average speed equals the speed.

Solved Examples on Speed Distance and Time:

1. Nancy travelled a distance of 455 km by car in 10 hours. Find the speed of the car.

Distance travelled by car = 455 km

Time taken                    = 10 hours

Therefore, speed            = $\frac{\textrm{Distance}}{\textrm{Time}}$

                                   = $\frac{455}{10}$ km/hr

                                   = 45.5 km per hour

2. Find the speed and average speed of a train which leaves Madras at 1 p.m. and reaches Vijayawada in the same day at 9 p.m. The distance between the two stations is 432 km and the total time for stoppage is 2 hours between these stations.

Total time taken = 9 -1, that is, 8 hours;

Time of stoppage = 2 hours, that is, actual time taken = 8 hours - 2 hours = 6 hours

Speed = $\frac{\textrm{Distance}}{\textrm{Time}}$

         = $\frac{432 km}{6 hr}$

         = $\frac{432}{6}$

         = 72 km/hr

Average speed = $\frac{\textrm{Total Distance}}{\textrm{Total Time}}$

                     = $\frac{432}{8}$ km/hr

                     = 54 km/hr

3. A car travels a distance of 595 km in 8 ½ hours. What is its speed?

Distance travelled = 595 km

Time taken to travel this distance = 8$\frac{1}{2}$ hours = $\frac{17}{2}$ hours

Speed of the car = $\frac{\textrm{Distance}}{\textrm{Time}}$

                        = $\frac{\frac{595}{17}}{2}$ km/hour

                        = $\frac{592 × 2}{17}$

                        = 70 km/hr

Therefore, the speed of the car = 70 km/hour.

4. A train covers a distance of 1417 km in 13 hours. Find the speed of the train.

Solution:

Distance = 1417 km

Time taken = 13 hours

Speed = $\frac{\textrm{Distance}}{\textrm{Time}}$

          = $\frac{1417 km}{13 hr}$

          = 109 km/hr.

5. A car is moving at a speed of 69 km/hr. Find the time taken by the car to cover a distance of 1173 km.

Solution:

Distance = 1173 km

Speed = 69 km/hr

Time = $\frac{\textrm{Distance}}{\textrm{Speed}}$

        = $\frac{1173 km}{69 km/hr}$

        = 9 hrs.

Note: km ÷ $\frac{\textrm{km}}{\textrm{hr}}$

      = km × $\frac{hr}{\not km}$

      = hr

6. A bus travels a speed of 59 km/hr. Find the distance covered by it in 7 hours.

Solution:

Speed = 59 km/hr

Time = 7 hrs

Distance = Speed × Time

             = 59 km/hr × 7 hrs

             = 413 km

Note: $\frac{km}{\not hr}$ × hr

      = km

7. A motorbike running at a speed of 63 km/hr. How many kilometres will it cover in in 5$\frac{2}{3}$ hours?

Solution:

Speed = 63 km/hr.

Time = 5$\frac{2}{3}$ hrs = $\frac{17}{3}$ hrs

Distance = Speed × Time

            = 63 km/hr × $\frac{17}{3}$ hr

            = $\frac{63 km/hr × 17 hr}{3}$

            = 357 km

Note: $\frac{km}{\not hr}$ × hr

      = km

Average Speed:

Sometimes, the speed of a moving object varies from time to time. In such cases, we calculate the average speed of the moving object.

Let us consider an example.

8. A train covers 86 km in the 1st hour, 90 km in the 2nd hour, 80 km in the 3rd hour and 84 km in the 4th hour. Find the average speed of the train.

Solution:

Total distance covered = 86 km + 90 km + 80 km + 84 km

                                 = 340 km

Total time taken = 4 hours

Average speed = \(\frac{\textrm{Distance}}{\textrm{Time}}\)

                      = $\frac{340 km}{4}$

                      = 85 km/hr

Worksheet on Speed Distance and Time

I. Calculate the speed in each case.

Answer:

I: 1. 133.34 km/hr

2. 150 m/min

3. 42 cm/sec

4. 75 cm/sec

5. 95 m/min

II. Calculate the distance covered in each case.

Answer:

II: 1. 242.67 km

2. 3075 metre

3. 960 cm

4. 40 km

5. 160 km

III. Calculate the time taken in each case.

Answer:

III: 1. 7 hrs

2. 41.78 hrs

3. 50 sec

4. 40 sec

5. 20 hrs

● Speed Distance and Time.

Express Speed in Different Units

To find Speed when Distance and Time are given.

To find the Distance when Speed and Time are given.

To find Time when Distance and Speed are given.

Worksheet on Expressing Speed in Different Units

Worksheet on Speed, Distance and Time.

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