Question

Question 1.

A cyclist cover 500 m in 100 seconds. Convert his speed in km/hr.

Question 2.

A man travels at a speed of 20 kmLhr in a car. How far will he travel in 50 mins.

Question 3.

The speed of a train is 72 km/hr. Find its speed in m/sec.

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Answer 1

1] A cyclist cover 500 m in 100 seconds. Convert his speed in km/hr.

We have,

• Distance (s) = 500 m
• Time (t) = 100 s

★ Speed = Distance/Time

→ Speed = 500 m ÷ 100 s

→ Speed = 5 m/s

But, we have to find speed in km/h. So,

• In order to convert m/s to km/h, we multiply the value by 18/5.

Hence,

$\implies\sf{Speed=\Bigg \lgroup \not{5} \times \dfrac{18}{\not{5}}\Bigg \rgroup \;kmh^{-1}}$

$\implies\boxed{\sf{\red{Speed=18 \; kmh^{-1}}}}$

Therefore, speed in km/h is 18 km/h.

$\rule{200}2$

2] A man travels at a speed of 20 km/hr in a car. How far will he travel in 50 mins.

We have,

• Speed (v) = 20 km/h
• Time taken (t) = 50 mins → 50/60 hr → 5/6 hr

To calculate : Distance covered in 50 mins.

Now, as we know that,

$\bigstar \;\boxed{\sf{Distance= Speed \times Time}}$

$\implies\sf{Distance = \Bigg \lgroup 20 \times \dfrac{5}{6} \Bigg \rgroup \; km }$

$\implies\sf{Distance = \Bigg \lgroup 10 \times \dfrac{5}{3} \Bigg \rgroup \; km }$

$\implies\sf{Distance = \Bigg \lgroup \dfrac{50}{3} \Bigg \rgroup \; km }$

$\implies\boxed{\sf{\red{Distance= 16.\bar{6} \; km}}}$

Therefore, distance covered in 50 mins is 16.$\bf \bar{6}$ km.

$\rule{200}2$

3] The speed of a train is 72 km/hr. Find its speed in m/sec.

We have,

• Speed (v) = 72 km/h

We have to convert it in m/s.

To convert km/h to m/s, we multiply the value by 5/18. So,

$\implies\sf{Speed = 72 \; kmh^{-1} }$

$\implies\sf{Speed=\Bigg \lgroup \cancel{72} \times \dfrac{5}{\cancel{18}}\Bigg \rgroup \;ms^{-1}}$

$\implies\sf{Speed = (4 \times 5) \; ms^{-1} }$

$\implies\boxed{\sf{\red{Speed= 20 \; ms^{-1}}}}$

Therefore, speed of the train in m/s is 20 m/s.

$\rule{200}2$

Learn More :

• Distance is the total length of the path covered by the body.
• It is a scalar quantity, i.e has only magnitude.
• SI unit of distance is metre (m).
• Distance = Speed × Time
• Speed is the distance covered per unit time.
• It is a scalar quantity.
• SI unit of speed is metres per second (m/s).
• Speed = Distance/Time
• To convert km/h to m/s, multiply the value by 5/18.
• To convert m/s to km/h, multiply the value by 18/5.

Answer 2

Answer:

QUESTION NO 1 :-

$\leadsto$ A cyclist cover 500 m in 100 seconds. Convert his speed in km/hr.

Given :-

$\leadsto$ A cyclist cover 500 m in 100 seconds.

To Find :-

$\leadsto$ What is the speed of a cyclist in km/h.

Formula Used :-

$\clubsuit$ Speed Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Speed =\: \dfrac{Distance}{Time}}}}$

Solution :-

Given :

• Distance = 500 m
• Time = 100 s

According to the question by using the formula we get,

$\leadsto \sf Speed =\: \dfrac{500}{100}$

$\leadsto \sf\bold{\purple{Speed =\: 5\: m/s}}$

Hence, the speed of a cyclist is 5 m/s .

But here, in the question we have to find the speed in km/h.

So,

Change the speed m/s into km/h :

$\dashrightarrow \sf Speed =\: 5\: m/s$

$\dashrightarrow \sf Speed =\: 5 \times \dfrac{18}{5}\: km/h\: \: \bigg[ \sf\bold{\pink{1\: m/s =\: \dfrac{18}{5}\: km/h}} \bigg]$

$\dashrightarrow \sf Speed =\: \dfrac{\cancel{90}}{\cancel{5}}\: km/h$

$\dashrightarrow \sf\bold{\red{Speed =\: 18\: km/h}}$

$\therefore$ The speed of a cyclist in km/h is 18 km/h .

QUESTION NO 2 :-

$\mapsto$ A man travels at a speed of 20 km/h in a car. How far will he travel in 50 mins.

Given :

$\mapsto$ A man travels at a speed of 20 km/h in a car.

To Find :-

$\mapsto$ How far will he travel in 50 mins.

Formula Used :-

$\clubsuit$ Distance Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Distance =\: Speed \times Time}}}$

Solution :-

First, we have to convert the time minutes into hour :

$\leadsto \sf Time =\: 50\: minutes$

$\leadsto \sf Time =\: \dfrac{5\cancel{0}}{6\cancel{0}}\: hours$

$\leadsto \sf Time =\: \dfrac{5}{6}\: hours$

$\leadsto \sf\bold{\purple{Time =\: 0.83\: hours}}$

Now, we have to find how far will he travel :

Given :

• Speed = 20 km/h
• Time = 0.83 hrs

According to the question by using the formula we get,

$\dashrightarrow \sf Distance =\: 20 \times 0.83$

$\dashrightarrow \sf\bold{\red{Distance =\: 16.6\: km}}$

$\therefore$ He travel in 50 mins is 16.6 km .

QUESTION NO 3 :-

$\leadsto$ The speed of a train is 72 km/h. Find its speed in m/s.

Given :-

$\leadsto$ The speed of a train is 72 km/h.

To Find :-

$\leadsto$ What is the speed of a train in m/s.

Solution :-

Given :

• Speed of train = 72 km/h

So, according to the question we have to convert the speed km/h into m/s :

$\dashrightarrow \sf Speed =\: 72\: km/h$

$\dashrightarrow \sf Speed =\: 72 \times \dfrac{5}{18}\: m/s\: \: \bigg\{ \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}} \bigg\}$

$\dashrightarrow \sf Speed =\: \dfrac{\cancel{360}}{\cancel{18}}\: m/s$

$\dashrightarrow \sf\bold{\red{Speed =\: 20\: m/s}}$

$\therefore$ The speed of a train in m/s is 20 m/s .

EXTRA IMPORTANT FORMULA :-

$\bigstar$ Distance Formula :

$\mapsto \sf\bold{\pink{Distance =\: Speed \times Time}}$

$\bigstar$ Time Formula :

$\mapsto \sf\bold{\green{Time =\: \dfrac{Distance}{Speed}}}$

$\bigstar$ Speed Formula :

$\mapsto \sf\bold{\red{Speed =\: \dfrac{Distance}{Time}}}$