Speed, Distance and Time

Convert each of the following speeds into m/sec:

(i) 90 km/hr

(ii) 27 km/hr

(iii) 315 km/hr

(iv) 16.2 km/hr

Answer

(i) 90 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$:

$\therefore 90 \text { km/hr} =\Big(90 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = (5 \times 5) \text{ m/sec} \\[1em] = 25 \text{ m/sec}$

Hence, the answer is 25 m/sec.

(ii) 27 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$:

$\therefore 27 \text { km/hr} = \Big(27 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(3 \times \dfrac{5}{2}\Big)\text{ m/sec} \\[1em] = \dfrac{15}{2}\text{ m/sec} \\[1em] = 7.5\text{ m/sec}$

Hence, the answer is 7.5 m/sec.

(iii) 315 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$:

$\therefore 315 \text { km/hr} = \Big(315 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \dfrac{1575}{18}\text{ m/sec} \\[1em] = 87.5\text{ m/sec}$

Hence, the answer is 87.5 m/sec.

(iv) 16.2 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$:

$\therefore 16.2 \text { km/hr} = \Big(16.2 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \dfrac{81}{18}\text{ m/sec} \\[1em] = 4.5\text{ m/sec}$

Hence, the answer is 4.5 m/sec.

Convert each of the following speeds into km/hr:

(i) 35 m/sec

(ii) 14 m/sec

(iii) 60 m/sec

(iv) 3.5 m/sec

Answer

(i) 35 m/sec

To convert m/sec to km/hr, multiply by $\dfrac{18}{5}$:

$\therefore 35 \text { m/sec} = \Big(35 \times \dfrac{18}{5}\Big)\text{ km/hr} \\[1em] = (7 \times 18) \text{ km/hr} \\[1em] = 126 \text{ km/hr}$

Hence, the answer is 126 km/hr.

(ii) 14 m/sec

To convert m/sec to km/hr, multiply by $\dfrac{18}{5}$:

$\therefore 14 \text { m/sec} = \Big(14 \times \dfrac{18}{5}\Big)\text{ km/hr} \\[1em] = \dfrac{252}{5}\text{ km/hr} \\[1em] = 50.4\text{ km/hr}$

Hence, the answer is 50.4 km/hr.

(iii) 60 m/sec

To convert m/sec to km/hr, multiply by $\dfrac{18}{5}$:

$\therefore 60 \text { m/sec} =\Big(60 \times \dfrac{18}{5}\Big)\text{ km/hr} \\[1em] = (12 \times 18) \text{ km/hr} \\[1em] = 216 \text{ km/hr}$

Hence, the answer is 216 km/hr.

(iv) 3.5 m/sec

To convert m/sec to km/hr, multiply by $\dfrac{18}{5}$:

$\therefore 3.5 \text { m/sec} = \Big(3.5 \times \dfrac{18}{5}\Big)\text{ km/hr} \\[1em] = \dfrac{63}{5}\text{ km/hr} \\[1em] = 12.6\text{ km/hr}$

Hence, the answer is 12.6 km/hr.

A car travels a distance of 258 km in 3 hours 35 minutes. What is the speed of the car?

Answer

Given:

Distance = 258 km

Time = 3 hours 35 mins

Let's convert Time to hours:

1 hour = 60 mins

∴ 3 hours 35 mins = $3\dfrac{35}{60} \text{ hr} = 3\dfrac{7}{12} \text{ hr} = \dfrac{43}{12} \text{ hr}$

And

$\text {Speed} = \dfrac{\text{Distance}}{\text{Time}} \\[1em] = \left(\dfrac{258}{\dfrac{43}{12}}\right)\text{ km/hr} \\[1em] = \Big(258 \times \dfrac{12}{43}\Big)\text{ km/hr} \\[1em] = 6 \times 12\text{ km/hr} \\[1em] = 72 \text{ km/hr}$

The speed of the car is 72 km/hr.

A train covers 14 km in 8 minutes. What is the speed of the train?

Answer

Given:

Distance = 14 km

Time = 8 minutes

Let's convert Time to hours:

1 hour = 60 mins

∴ 8 minutes = $\dfrac{8}{60} \text{ hr} = \dfrac{2}{15} \text{ hr}$

And

$\text {Speed} = \dfrac{\text{Distance}}{\text{Time}} \\[1em] = \left(\dfrac{14}{\dfrac{2}{15}}\right)\text{ km/hr} \\[1em] = \Big(14 \times \dfrac{15}{2}\Big)\text{ km/hr} \\[1em] = 7 \times 15\text{ km/hr} \\[1em] = 105 \text{ km/hr}$

The speed of the train is 105 km/hr.

A man can walk 8 km in 1 hour 15 minutes. Find his speed.

Answer

Given:

Distance = 8 km

Time = 1 hour 15 minutes

Let's convert Time to hours

1 hour = 60 mins

∴ 1 hour 15 minutes = $1\dfrac{15}{60} \text{ hr} = 1\dfrac{1}{4} \text{ hr} = \dfrac{5}{4} \text{ hr}$

And

$\text {Speed} = \dfrac{\text{Distance}}{\text{Time}} \\[1em] = \left(\dfrac{8}{\dfrac{5}{4}}\right)\text{ km/hr} \\[1em] = \Big(8 \times \dfrac{4}{5}\Big)\text{ km/hr} \\[1em] = \dfrac{32}{5}\text{ km/hr} \\[1em] = 6.4 \text{ km/hr}$

The speed of the man is 6.4 km/hr.

Rahul cycles at 12 km per hour. How much distance does he cover in 36 minutes?

Answer

Given:

Speed = 12 km/hr

Time = 36 minutes

Let's convert Time to hours:

1 hour = 60 mins

∴ 36 minutes = $\dfrac{36}{60} \text{ hr} = \dfrac{3}{5} \text{ hr}$

And

Distance = Speed x Time

Substituting the values in above, we get:

$\text {Distance} = \Big(12 \times \dfrac{3}{5}\Big)\text{ km} \\[1em] = \dfrac{36}{5}\text{ km} \\[1em] = 7.2 \text{ km}$

The distance covered by Rahul is 7.2 km.

Ravi walks at a uniform speed of 4 km per hour. How much time does he take to cover 600 metres?

Answer

Given:

Speed = 4 km/hr

Distance = 600 metres

Let's convert Distance to km:

1 km = 1000 m

∴ 600 m = $\dfrac{600}{1000} \text{ km} = 0.6 \text{ km}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

Time = $\dfrac{0.6}{4}$ hours = 0.15 hours

Let's convert time to minutes:

1 hour = 60 minutes

∴ 0.15 hours = 0.15 x 60 minutes = 9 minutes

The time taken by Ravi is 9 minutes.

A train is running at 45 km per hour. How far does it go in 8 seconds?

Answer

Given:

Speed = 45 km/hr

Let's convert speed into m/sec:

$45 \text { km/hr} = \Big(45 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \dfrac{225}{18}\text{ m/sec} \\[1em] = 12.5\text{ m/sec}$

Time = 8 seconds

Distance = Speed x Time

Substituting the values in above, we get:

Distance = 12.5 x 8 m = 100 m

The distance covered by train is 100 m.

Which is more : a speed of 36 km/hr or a speed of 10.5 m/sec?

Answer

Let's convert 36 km/hr into m/sec:

$36 \text { km/hr} = \Big(36 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = (2 \times 5)\text{ m/sec} \\[1em] = 10 \text{ m/sec}$

Now, compare 10 m/sec and 10.5 m/sec:

10.5 m/sec > 10 m/sec

10.5 m/sec is more.

A car, running at 45 km/hr takes 6 hours to cover a journey. At what speed must it travel to complete the journey in 5 hours?

Answer

Given:

Speed = 45 km/hr

Time = 6 hours

Distance = Speed x Time

Substituting the values in above, we get:

Distance = 45 x 6 km = 270 km

Now, let's find the required speed for the new time:

Distance = 270 km, New Time = 5 hours

New Speed = $\dfrac{\text{Distance}}{\text{New Time}}$

Substituting the values in above, we get:

New Speed = $\dfrac{270}{5}$ km/hr

New Speed = 54 km/hr

Speed of the car to complete the journey in 5 hours is 54 km/hr.

A car covers a certain distance in 50 minutes if it runs at 45 km per hour. How much time will it take to cover the same distance at a speed of 30 km per hour?

Answer

Given:

Speed = 45 km/hr

Time = 50 minutes

Let's convert time to hour:

1 hour = 60 minutes

∴ 50 minutes = $\dfrac{50}{60}\text{ hr} = \dfrac{5}{6}\text{ hr}$

Distance = Speed x Time

Substituting the values in above, we get:

Distance = $45 \times \dfrac{5}{6}$ km = $\dfrac{225}{6}$ km

Let's find the time for the new speed:

Distance = $\dfrac{225}{6}$ km, New Speed = 30 km/hr

Time = $\dfrac{\text{Distance}}{\text{New Speed}}$

Substituting the values in above, we get:

Time = $\dfrac{\dfrac{225}{6}}{30}\text{ hours}$

$= \Big(\dfrac{225}{6} \times \dfrac{1}{30}\Big)\text{ hours} \\[1em] = \Big(\dfrac{45}{6} \times \dfrac{1}{6}\Big)\text{ hours} \\[1em] = \dfrac{45}{36} \text{ hours} \\[1em] = 1.25 \text{ hours}$

1.25 hours = 1 hour + (0.25 x 60) minutes = 1 hour 15 minutes

Time taken by the car is 1 hour 15 minutes.

A bus covers 100 km in first 2 hours, 64 km in the next 1 hour and 72 km in the next 2 hours. Find the average speed of the bus during the whole journey.

Answer

Given:

Distance : (D1) = 100 km, (D2) = 64 km, (D3) = 72 km

Time : (T1) = 2 hrs, (T2) = 1 hr, (T3) = 2 hrs

Total Distance = 100 km + 64 km + 72 km = 236 km

Total Time = 2 hrs + 1 hrs + 2 hrs = 5 hrs

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average Speed = $\dfrac{236}{5}$ km/hr = 47.2 km/hr

Average speed of the bus is 47.2 km/hr.

An aeroplane covers 2500 km, 1200 km and 500 km at the rate of 500 km/hr, 400 km/hr and 250 km/hr respectively. Find its average speed for the whole journey.

Answer

Given:

Distances: (D1) = 2500 km, D2 = 1200 km, D3 = 500 km

Speed: (S1) = 500 km/hr, (S2) = 400 km/hr, (S3) = 250 km/hr

Let's find time taken for each part:

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

T1 = $\dfrac{D1}{S1} = \dfrac{2500}{500}$ = 5 hrs

T2 = $\dfrac{D2}{S2} = \dfrac{1200}{400}$ = 3 hrs

T3 = $\dfrac{D3}{S3} = \dfrac{500}{250}$ = 2 hrs

Total Distance = 2500 km + 1200 km + 500 km = 4200 km

Total Time = 5 hrs + 3 hrs + 2 hrs = 10 hrs

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average Speed = $\dfrac{4200}{10}$ km/hr = 420 km/hr

Average speed of the aeroplane is 420 km/hr.

A scooterist travels at 36 km/hr for 5 hours and at 45 km/hr for 4 hours. Find his average speed for the whole journey.

Answer

Given:

Speed: S1 = 36 km/hr, S2 = 45 km/hr

Time: T1 = 5 hrs, T2 = 4 hrs

Let's find distance covered in each part:

Distance = Speed x Time

D1 = S1 x T1 = 36 x 5 = 180 km

D2 = S2 x T2 = 45 x 4 = 180 km

Total Distance = 180 km + 180 km = 360 km

Total Time = 5 hrs + 4 hrs = 9 hrs

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average Speed = $\dfrac{360}{9}$ km/hr = 40 km/hr

Average speed of the scooterist is 40 km/hr.

Raju's school is 4 km away from his house. He walks from his house to school and comes back in $2\dfrac{1}{2}$ hours. Find his average speed.

Answer

Given:

Distance (one way) = 4 km

Total Distance = 4 km (to school) + 4 km (back home) = 8 km

Total Time = $2\dfrac{1}{2} \text{ hours} = 2.5 \text{ hours}$

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average Speed = $\dfrac{8}{2.5}$ km/hr = 3.2 km/hr

Average speed of Raju is 3.2 km/hr.

Find the time taken by a train 150 m long, running at 60 km/hr in crossing a man standing on the platform.

Answer

Given:

Distance = Length of train = 150 m

Speed = 60 km/hr

Let's convert speed to m/sec:

$60 \text { km/hr} = \Big(60 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(10 \times \dfrac{5}{3}\Big)\text{ m/sec} \\[1em] = \dfrac{50}{3} \text{ m/sec}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

$\text {Time} = \dfrac{150}{\dfrac{50}{3}} \text{ seconds} \\[1em] = 150 \times \dfrac{3}{50}\text{ seconds} \\[1em] = 3 \times \dfrac{3}{1}\text{ seconds} \\[1em] = 3 \times 3\text{ seconds} \\[1em] = 9 \text{ seconds}$

Hence, the train will cross a man in 9 seconds.

The length of a train is 175 m. It is running at 63 km/hr. In how much time would it cross an electric pole?

Answer

Given:

Distance = Length of train = 175 m

Speed = 63 km/hr

Let's convert speed to m/sec:

$63 \text { km/hr} = \Big(63 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(7 \times \dfrac{5}{2}\Big)\text{ m/sec} \\[1em] = \dfrac{35}{2} \text{ m/sec}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

$\text {Time} = \dfrac{175}{\dfrac{35}{2}} \\[1em] = 175 \times \dfrac{2}{35}\text{ seconds} \\[1em] = 5 \times \dfrac{2}{1}\text{ seconds} \\[1em] = 5 \times 2\text{ seconds} \\[1em] = 10 \text{ seconds}$

Hence, the train will cross an electric pole in 10 seconds.

A train 150 m long crosses a tree in 6 seconds. What is the speed of the train in km per hour?

Answer

Given:

Distance = Length of train = 150 m

Time = 6 seconds

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting the values in above, we get:

Speed = $\dfrac{150}{6}$ m/sec = 25 m/sec

Let's convert speed to km/hr:

$\therefore 25 \text{ m/sec} = 25 \times \dfrac{18}{5} \text{ km/hr} \\[1em] = 5 \times \dfrac{18}{1} \text{ km/hr} \\[1em] = 5 \times 18 \text{ km/hr} \\[1em] = 90 \text{ km/hr}$

Hence, speed of the train is 90 km/hr.

A train 120 m long is running at 54 km per hour. In how much time will it pass a bridge 180 m long?

Answer

Given:

Distance (D1) = Length of train = 120 m

Distance (D2) = Length of bridge = 180 m

Total Distance = 120 m + 180 m = 300 m

Speed = 54 km/hr

Let's convert speed to m/sec:

$54 \text { km/hr} = \Big(54 \times \dfrac{5}{18}\Big) \text{ m/sec} \\[1em] = \Big(3 \times \dfrac{5}{1}\Big) \text{ m/sec} \\[1em] = 15 \text{ m/sec}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

Time = $\dfrac{300}{15}$ seconds = 20 seconds

Hence, the train will pass a bridge in 20 seconds.

A train 760 m long crosses a platform 440 m long in 40 seconds. Find the speed of the train in km per hour.

Answer

Given:

Distance (D1) = Length of train = 760 m

Distance (D2) = Length of platform = 440 m

Total Distance = 760 m + 440 m = 1200 m

Time = 40 seconds

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting the values in above, we get:

Speed = $\dfrac{1200}{40}$ m/sec = 30 m/sec

Let's convert speed to km/hr:

$\therefore 30\text{ m/sec} = 30 \times \dfrac{18}{5} \text{ km/hr} \\[1em] = 6 \times \dfrac{18}{1} \text{ km/hr} \\[1em] = 6 \times 18 \text{ km/hr} \\[1em] = 108 \text{ km/hr}$

Hence, speed of the train is 108 km/hr.

Which of the following is correct?

1. Distance = Speed x Time

2. Time = Distance x Speed

3. Speed = Distance x Time

4. Time = $\dfrac{\text {Speed}}{\text {Distance}}$

Answer

Distance = Speed x Time is correct.

All other options are incorrect.

Hence, option 1 is the correct option.

To convert a speed of km/hr into m/sec, we multiply it by

1. $\dfrac{8}{15}$

2. $\dfrac{18}{5}$

3. $\dfrac{5}{18}$

4. $\dfrac{15}{8}$

Answer

To convert a speed of km/hr into m/sec, we multiply it by $\dfrac{5}{18}$.

Because, 1 km = 1000 m and 1 hr = 3600 sec.

$\dfrac{1000}{3600} = \dfrac{5}{18}$

Hence, option 3 is the correct option.

A car is moving with a speed of 90 km/hr. Its speed in m/sec is

1. 15 m/sec
2. 25 m/sec
3. 35 m/sec
4. 45 m/sec

Answer

Given:

Speed = 90 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$:

$90 \text { km/hr} = \Big(90 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(5 \times \dfrac{5}{1}\Big)\text{ m/sec} \\[1em] = (5 \times 5)\text{ m/sec} \\[1em] = 25 \text{ m/sec}$

Hence, option 2 is the correct option.

An athlete runs at 30 km/hr. In how much time will he run a race of 200 metres?

1. 20 sec
2. 24 sec
3. 32 sec
4. 36 sec

Answer

Given:

Speed = 30 km/hr, Distance = 200 m

Let's convert 30 km/hr to m/sec:

$30 \text { km/hr} = \Big(30 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(5 \times \dfrac{5}{3}\Big)\text{ m/sec} \\[1em] = \Big(\dfrac{25}{3}\Big)\text{ m/sec}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

$\text {Time} = \dfrac{200}{\dfrac{25}{3}} \text {seconds} \\[1em] = 200 \times {\dfrac{3}{25}} \text{ seconds} \\[1em] = 8 \times {\dfrac{3}{1}} \text{ seconds} \\[1em] = 8 \times 3 \text{ seconds} \\[1em] = 24 \text{ seconds}$

Hence, option 2 is the correct option.

A car is moving at a speed of 48 km/hr. How many metres will it travel in 15 minutes?

1. 8000 m
2. 10000 m
3. 12000 m
4. 16000 m

Answer

Given:

Speed = 48 km/hr, Time = 15 mins

Let's convert time to hrs:

1 hr = 60 mins

Time = 15 mins = $\dfrac{15}{60} \text{ hr} = \dfrac{1}{4} \text{ hr}$

Distance = Speed x Time

Substituting the values in above, we get:

Distance = $48 \times \dfrac{1}{4}$ km

Distance = 12 x 1 km = 12 km

Let's convert 12 km to meters:

1 km = 1000 m

Distance = 12 km = 12 x 1000 m = 12000 m

Hence, option 3 is the correct option.

A cyclist covers 175 metres in 25 seconds. What is his speed in km per hour?

1. 35 km/hr
2. 33.6 km/hr
3. 27 km/hr
4. 25.2 km/hr

Answer

Given:

Distance = 175 m, Time = 25 seconds

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting the values in above, we get:

Speed = $\dfrac{175}{25}$ m/sec = 7 m/sec

Let's convert 7 m/sec to km/hr:

$7 \text{ m/sec} = 7 \times \dfrac{18}{5} \text{ km/hr} \\[1em] = \dfrac{126}{5} \text{ km/hr} \\[1em] = 25.2 \text{ km/hr}$

Hence, option 4 is the correct option.

A car covers 108 km in first two hours and 90 km in the next one hour. Its average speed is

1. 28 km/hr
2. 33 km/hr
3. 66 km/hr
4. 99 km/hr

Answer

Given:

Distances: (D1) = 108 km, (D2) = 90 km

Time: (T1) = 2 hrs, (T2) = 1 hr

Total Distance = 108 km + 90 km = 198 km

Total Time = 2 hrs + 1 hr = 3 hrs

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average Speed = $\dfrac{198}{3}$ km/hr = 66 km/hr

Hence, option 3 is the correct option.

Fill in the blanks :

(i) A speed of 81 km/hr expressed in metres/sec is ............... .

(ii) Which is greater — a speed of 50 m/sec or 50 km/hr? ............... .

(iii) If a moving body covers equal distances in equal intervals of time, its speed is said to be ............... .

(iv) In crossing a platform, a train has to cover a distance equal to the ............... of the lengths of the train and the platform.

(v) To convert a speed of m/sec into km/hr, we multiply it by ............... .

Answer

(i) A speed of 81 km/hr expressed in metres/sec is 22.5 m/sec.

(ii) Which is greater — a speed of 50 m/sec or 50 km/hr? 50 m/sec.

(iii) If a moving body covers equal distances in equal intervals of time, its speed is said to be uniform.

(iv) In crossing a platform, a train has to cover a distance equal to the sum of the lengths of the train and the platform.

(v) To convert a speed of m/sec into km/hr, we multiply it by $\dfrac{18}{5}$.

Explanation

(i)

Given:

Speed = 81 km/hr

To convert km/hr to m/sec, multiply by $\dfrac{5}{18}$.

$81 \text { km/hr}= \Big(81 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(9 \times \dfrac{5}{2}\Big)\text{ m/sec} \\[1em] = \dfrac{45}{2}\text{ m/sec} \\[1em] = 22.5 \text{ m/sec}$

Speed = 22.5 m/sec

(ii)

Let's convert 50 km/hr into m/sec:
$50 \text { km/hr} = \Big(50 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \dfrac{250}{18}\text{ m/sec} \\[1em] ≈ 13.89 \text{ m/sec}$

Now compare 50 m/sec and 13.89 m/sec,

50 m/sec > 13.89 m/sec

So, 50 m/sec is greater.

(iii) The given statement is the definition of Uniform Speed (or constant speed). If the distance covered doesn't change for every second or minute that passes, the speed is consistent.

(iv) To completely clear a platform, the front of the train must enter the platform, travel the platform's length, and then the back of the train must travel the train's own length to fully exit.

(v) Since $1 \text{ m} = \dfrac{1}{1000}\text{ km}$ and $1 \text{ sec} = \dfrac{1}{3600}\text{ hr}$, the conversion factor simplifies to $\dfrac{3600}{1000} = \dfrac{18}{5}$.

Write true (T) or false (F) :

(i) A speed of 45 km/hr is the same as $12\dfrac{1}{3}$ m/s.

(ii) Average speed = $\dfrac{\text{Total distance covered}}{\text{Total time taken}}$

(iii) If a moving body covers unequal distances in equal intervals of time, its speed is said to be instantaneous.

(iv) A speed of 1 km/hr is equal to a speed of $\dfrac{5}{18}$ m/s.

(v) A 240 m long train crosses a platform double its length in 54 sec. Then, the speed of the train is 60 km.

Answer

(i) False
Reason —

To convert 45 km/hr to m/s, multiply by $\dfrac{5}{18}$.

$45 \text { km/hr} = \Big(45 \times \dfrac{5}{18}\Big)\text{ m/s} \\[1em] = \Big(5 \times \dfrac{5}{2}\Big)\text{ m/s} \\[1em] = \dfrac{25}{2}\text{ m/s} \\[1em] = 12.5 \text{ m/s}$

Let's convert $12\dfrac{1}{3}$ m/s to decimal:

$12\dfrac{1}{3}\text{ m/s} = \dfrac{37}{3}\text{ m/s} = 12.33 \text{ m/s}$

12.5 m/s is not the same as $12\dfrac{1}{3} \text{ m/s } (12.33)\text{ m/s}$.

(ii) True
Reason —

Average speed = $\dfrac{\text{Total distance covered}}{\text{Total time taken}}$

This is the standard mathematical definition for Average Speed, used to calculate the speed over a journey with multiple parts.

(iii) False
Reason — If the distances are unequal, the speed is called Non-uniform or Variable speed. "Instantaneous speed" refers to the speed at a specific moment in time (like what a car's speedometer shows).

(iv) True
Reason — To convert km/hr to m/s, multiply by $\dfrac{5}{18}$.

Speed = 1 km/hr = $\Big(1 \times \dfrac{5}{18}\Big)\text{ m/s} = \dfrac{5}{18} \text{ m/s}$

(v) False
Reason —

Train length = 240 m

Platform length = 2 x 240 = 480 m

Total Distance = 240 m + 480 m = 720 m

Time = 54 sec

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting values in the above, we get:

Speed = $\dfrac{720 \text{ m}}{54 \text{ sec}} = \dfrac{40}{3} \text{ m/s}$

Let's convert speed to km/hr:

$\dfrac{40}{3} \text{ m/s} = \Big(\dfrac{40}{3} \times \dfrac{18}{5}\Big)\text{ km/hr} \\[1em] = (8 \times 6)\text{ km/hr} \\[1em] = 48 \text{ km/hr}$

Kapil is an expert cyclist. Every morning he starts from his home on his cycle and rides on the road running parallel to the railway track, to reach the railway crossing, 27 km away from his home.

(1) Today he managed to reach the railway crossing in 3 hours. Find his speed in m/sec :

1. 2 m/sec
2. 2.5 m/sec
3. 3 m/sec
4. 4.5 m/sec

(2) If tomorrow he wishes to cover this distance in 2 hours, by how much does he need to increase his speed ?

1. 1.25 m/s
2. 1.5 m/s
3. 1.75 m/s
4. 2.25 m/s

(3) Today, he has to stop at the railway crossing for a train to pass. What time will the train 180 m long, running at 54 km per hour take to pass him :

1. 9 sec
2. 10 sec
3. 12 sec
4. 15 sec

(4) What time will this train take to pass a platform 300 m long at the speed of 10 m/s?

1. 30 sec
2. 32 sec
3. 36 sec
4. 35 sec

Answer

(1)

Given:

Distance = 27 km = 27 x 1000 m = 27000 m

Time = 3 hours = 3 x 3600 sec = 10800 sec

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting values in the above, we get:

Speed = $\dfrac{27000}{10800}\text{ m/sec} = \dfrac{270}{108}\text{ m/sec} = 2.5\text{ m/sec}$

Hence, option 2 is the correct option.

(2)

Given:

Distance = 27000 m

Time = 2 hours = 2 x 3600 sec = 7200 sec

Old Speed = 2.5 m/sec

New Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Substituting values in the above, we get:

New Speed = $\dfrac{27000}{7200}\text{ m/sec} = \dfrac{270}{72}\text{ m/sec} = 3.75\text{ m/sec}$

Let's calculate the increase in speed:

Increase = New Speed - Old Speed

Increase = 3.75 m/sec - 2.5 m/sec = 1.25 m/sec

Hence, option 1 is the correct option.

(3)

Given:

Distance = Train length = 180 m

Speed = 54 km/hr

Let's convert speed to m/sec:

$54 \text { km/hr} = \Big(54 \times \dfrac{5}{18}\Big)\text{ m/sec} \\[1em] = \Big(3 \times \dfrac{5}{1}\Big)\text{ m/sec} \\[1em] = 15 \text{ m/sec}$

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Substituting the values in above, we get:

Time = $\dfrac{180}{15}\text{ sec} = 12 \text{ sec}$

Hence, option 3 is the correct option.

(4)

Given:

Train length = 180 m

Platform length = 300 m

Total Distance = 180 m + 300 m = 480 m

Speed = 10 m/sec

Time = $\dfrac{\text{Total Distance}}{\text{Speed}}$

Substituting values in the above, we get:

Time = $\dfrac{480}{10}\text{ sec} = 48 \text{ sec}$

Time taken by the train to pass the platform is 48 sec.

Therefore, none of the provided options is correct for the given values.

Assertion: A car is travelling at a speed of 48 km/h. In 35 minutes, it will cover 28 km.

Reason: Distance = speed x time

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation

Given:

Speed = 48 km/hr

Distance = 28 km

Time = 35 minutes

Let's convert time to hours:

1 hour = 60 minutes

Time = 35 minutes = $\dfrac{35}{60}\text{ hr} = \dfrac{7}{12}\text{ hr}$

Distance = Speed x Time

Substituting the values in above, we get:

Distance = $\Big(48 \times \dfrac{7}{12}\Big)\text{ km} = \Big(4 \times \dfrac{7}{1}\Big)\text{ km} = 28 \text{ km}$

The Assertion is True.

Reason:

Distance = speed x time

This is the correct, standard formula for distance.

Hence, option 1 is the correct option.

Assertion: Vivek goes from his village to a city at 6 km/h and returns back at a speed of 4 km/h. If the distance between village and the city is 12 km, then his average speed for the whole journey is 4.8 km/h.

Reason: Average speed = $\dfrac{\text{Onward speed + return speed}}{2}$

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

Assertion (A) is true but Reason (R) is false.

Explanation

Given:

Distance = 12 km

Onward speed = 6 km/hr

Return speed = 4 km/hr

Let's find total time:

Onward time (T1) = $\dfrac{\text{Distance}}{\text{Onward speed}} = \dfrac{12}{6}\text{ hrs} = 2 \text{ hrs}$

Return time (T2) = $\dfrac{\text{Distance}}{\text{Return speed}} = \dfrac{12}{4}\text{ hrs} = 3 \text{ hrs}$

Total Time = 2 hrs + 3 hrs = 5 hrs

Total Distance = 12 km (to city) + 12 km (back home) = 24 km

Average speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

Substituting the values in above, we get:

Average speed = $\dfrac{24}{5}\text{ km/hr} = 4.8 \text{ km/hr}$.

The Assertion is True.

Reason:

Average speed = $\dfrac{\text{Onward speed + return speed}}{2}$

This is False. You cannot simply find the average of the speeds. You must always use $\dfrac{\text{Total Distance}}{\text{Total Time}}$.

The reason is false.

Hence, option 3 is the correct option.