**Motion Worksheet-4**

- A car covers a distance of 3 kilometres in 5 minutes. Calculate his speed in :

kilometres per hour (km/h)

A. 36 B. 18 C. 10 D. 72

- A man travels a distance of 1.5 m towards East, then 2.0 m towards south and finally 4.5 m towards east.

What is the resultant displacement in this case? ( in meters)

A. 8 B. 6.3 C. 4.5 D. 9

- The train ‘A’ traveled a distance of 120 km in 3 hours whereas another train ‘B’ traveled a distance of 180 km in 4 hours. Which train traveled faster?

A. Train A B. Train B

C. Both will be same D. Can’t say

- A car travels 30 km at a uniform speed of 40/h and the next 30 km at a uniform speed of 20 km/h. Find the average speed of car in kmph.

A. 26.6 B. 28 C. 30 D. 25.5

- On a 120 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must the train travel the next 90 km so as to average 60 km/h for the entire trip ?

A. 80 km/h. B. 120 km/h.

C. 100 km/h. D. 90 km/h.

**Answer:**

- A

**Explanation: **Here we will discuss to convert the speed in cm/sec, m/sec and km/h

In order to calculate the speed in centimeters per second first of all we should convert the given distance of 3 kilometres into centimeters and the given time of 5 minutes into seconds.

Note that 1 kilometre has 1000 metres and 1 metre has 100 centimetres. Now,

Distance traveled = 3 km

= 3 × 1000 m

= 3 × 1000 × 100 cm

= 300,000 cm ……(1)

Time taken = 5 minutes

= 5 × 60 seconds

= 300 s ……(2)

Speed =

= 1000 cm/s ……(3)

Thus, the speed of car is 1000 centimetres per second.

(b) To express the speed in metres per second we need to convert the given distance of 3 kilometres into metres and the given time of 5 minutes into seconds. so in this case :

Distance traveled = 3 km

= 3 × 1000 m

= 3000 m ……(4)

Time taken = 5 minutes

= 5 × 60 seconds

= 300 s ……(5)

Now, Speed =

=

= 10 m/s ……(6)

So, the speed of car is 10 metres per second.

(c) To calculate the speed in kilometers per hour, we need to express the given distance in kilometers and the given time in hours. So, in this case :

Distance traveled = 3 km …….(7)

We know that, Speed

= 36 km/h ……..(8)

Thus, the speed of car is 36 kilometres per hour.

- B

**Explanation: **(i) Total distance traveled by the person is

= 1.5 + 2.0 + 4.5

= 8.0 m

(ii) To find the resultant displacement we need to draw a map of the man’s movements by choosing a scale.

Let 1 cm represents 1 m. So 1.5 m can be represented by 1.5 cm long line, 2.0 m by 2.0 cm line and 4.5 m by a 4.5 cm line.

We can draw a 1.5 cm line AB from west to east to represent 1.5 m towards east. Then we draw a 2.0 cm long line BC towards south to represent 2.0 m towards south. And then we draw a third line CD, 4.5 cm long, towards east to represent a distance of 4.5 m towards east.

Now, the resultant displacement can be found by joining the starting point A with the finishing point D. That means line AD represent the final displacement of the person. If we measure the length of line AD. It is found to be 6.3 cm.

Now, 1 cm = 1 m

So, 6.3 cm = 6.3 m

Thus, the final displacement of the person as represented by AD is 6.3 metres.

- B

**Explanation: **In this case we have to calculate the speeds of both the trains separately. The train having higher speed will travel faster.

(i) We know that : Speed =

Now, Distance traveled by train A = 120 km

Time taken by train A = 3 hours

So, Speed of train A =

= 40 km/h …..(1)

Thus, the speed of train A is 40 kilometres per hour.

(ii) Now, Distance traveled by train B = 180 km

Time taken by train B = 4 h

Speed of train B =

= 45 km/h ……(2)

Thus, the speed of train B is 45 kilometres per hour.

Since the speed of train B is higher, therefore, train B travels faster.

- A

**Explanation: **(i) First the car travels a distance of 30 kilometres at a speed of 40 kilometres per hour. Let us find out the time taken by the car to travel this distance.

Here, Speed = 40 km/h

Distance = 30 km

And, Time = ?

Now, Speed = distance / time

So, 40 = 40/Time

And, Time = 30/40 hours

Or, Time (t_{1}) = 3/4 hours ……..(1)

(ii) Next the car travels a distance of 30 km at a speed of 20 km/h.

In this case :

Speed = 20 km/h

Distance = 30 km

And, Time = ?

Speed = distance / time

So, 20 = (30/time)

And, Time = 30/20 hours

Or Time (t_{2}) = (3/2) hours …….(2)

We can get the total time taken by the car for the whole journey

Total time taken = (3/4) + (3/2) hours

= (3+6)/4 hours

= 9/4 hours ……..(3)

Total distance traveled = 30 km + 30 km

= 60 km ……..(4)

Now, Average speed =

= (240/9) = 26.6 km/h

So the average speed of the car for the whole journey is 26.6 kilometres per hour.

- D

**Explanation: **In this problem the total distance traveled by the train (which is 120 km) is given, and the average speed of the train for the whole journey (which is 60 km/h) is given. From these two values we can calculate the total time taken by the train for the entire journey.

We know that, Average speed

So,

And, Total time taken hours = 2 hours

We will now calculate the time taken by the train for the first 30 km journey, and the next 90 km journey, separately (see figure ).

(i) For the first part of the train journey, we have :

Speed = 30 km/h

Distance = 30 km

And, Time = ?

Now, Speed

So,

And, time taken = (30/30) hours

= 1 hour ………(2)

(ii) for the second part of the train journey, let us suppose that the speed of the train is x km/h. So, for the second part of the train journey, we have :

Speed = x km/h (Supposed)

Distance = 90 km

And, Time = ?

Now, Speed

So,

And, Time taken = (90/x) hours ………(3)

Now, adding equations (2) and (3), we get the total time taken for the entire trip :

Total time taken = 1+(90/x) hours ……..(4)

We know that that the total time taken for the entire trip is 2 hours. That means equation (4) must be equal to 2.

And x = 90 km/h

Thus, the train should travel the next 90 km distance at a speed of 90 km/h.