Question

Convert each of the following speed into m/sec:
(i) 72 km/h
(ii) 12.6 km/h
(iii) 23.4 km/h
(iv) 306 km/h
2. Convert each of the following speed into km/hr:
(i) 45 m/sec
(ii) 4 m/sec
(iii) 1.5 m/sec
(iv) 2.8 m/sec
(v) 22.5 m/sec
3. Which is greater – a speed of 24 km/h or a speed of 12.8 m/sec?
4. Ron covers a distance of 1710 m in 3 minutes. Find his speed in km/hr.

Answer 1

Therefore to calculate the speed in m/s we need to multiply 72 km/h with 10003600. ⇒72km/h=20m/s.

Answer 2

$\underline{\underline{\Large{\pmb{\frak{Explanation : }}}}}$

Convert each of the following speed into m/s:

To convert the speed from km/h to m/s. We multiply it by 5/18.

[ i ]

$\dashrightarrow \quad \rm { 72 \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 72 \; km \: h^{-1} = \Bigg (72\times \dfrac{5}{18} \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 72 \; km \: h^{-1} = \Bigg( 4\times 5 \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 72 \; km \: h^{-1} = 20 \; m \: s^{-1}}} } \; \bigstar$

[ ii ]

$\dashrightarrow \quad \rm { 12.6 \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 12.6 \; km \: h^{-1} = \Bigg (12.6 \times \dfrac{5}{18} \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 12.6 \; km \: h^{-1} = \Bigg( 0.7 \times 5 \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 12.6 \; km \: h^{-1} = 3.5 \; m \: s^{-1}}} } \; \bigstar$

[ iii ]

$\dashrightarrow \quad \rm { 23.4 \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 23.4 \; km \: h^{-1} = \Bigg( 23.4 \times \dfrac{5}{18} \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 23.4 \; km \: h^{-1} = \Bigg( 1.3 \times 5 \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 23.4 \; km \: h^{-1} = 6.5 \; m \: s^{-1}}} } \; \bigstar$

[ iv ]

$\dashrightarrow \quad \rm { 306 \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 306 \; km \: h^{-1} = \Bigg (306 \times \dfrac{5}{18} \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 306 \; km \: h^{-1} = \Bigg (17 \times 5 \Bigg ) \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf {306 \; km \: h^{-1} = 85 \; m \: s^{-1}}} } \; \bigstar$

$\rule{200}2$

2. Convert each of the following speed into km/hr:

To convert m/s to km/h, we multiply it by 18/5.

[ i ]

$\dashrightarrow \quad \rm {45 \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 45 \; m \: s^{-1} = \Bigg( 45\times \dfrac{18}{5} \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 45 \; m \: s^{-1} = \Bigg ( 9 \times 18 \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 45 \; m \: s^{-1} = 162 \; km \: h^{-1}}} } \; \bigstar$

[ ii ]

$\dashrightarrow \quad \rm {4 \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 4 \; m \: s^{-1} = \Bigg( 4 \times \dfrac{18}{5} \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 4 \; m \: s^{-1} = \Bigg ( 0.8 \times 18 \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 4 \; m \: s^{-1} = 14.4 \; km \: h^{-1}}} } \; \bigstar$

[ iii ]

$\dashrightarrow \quad \rm {1.5 \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 1.5 \; m \: s^{-1} = \Bigg( 1.5 \times \dfrac{18}{5} \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 1.5 \; m \: s^{-1} = \Bigg ( 0.3 \times 18 \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 1.5 \; m \: s^{-1} = 5.4 \; km \: h^{-1}}} } \; \bigstar$

[ iv ]

$\dashrightarrow \quad \rm {2.8 \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 2.8 \; m \: s^{-1} = \Bigg( 2.8 \times \dfrac{18}{5} \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 2.8 \; m \: s^{-1} = \Bigg ( 0.56 \times 18 \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 2.8 \; m \: s^{-1} = 10.08 \; km \: h^{-1}}} } \; \bigstar$

[ v ]

$\dashrightarrow \quad \rm {22.5 \; m \: s^{-1} } \\ \\ \dashrightarrow \quad \rm { 22.5 \; m \: s^{-1} = \Bigg( 22.5 \times \dfrac{18}{5} \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \rm { 22.5 \; m \: s^{-1} = \Bigg ( 4.5 \times 18 \Bigg ) \; km \: h^{-1} } \\ \\ \dashrightarrow \quad \underline{\boxed{\bf { 22.5 \; m \: s^{-1} = 81 \; km \: h^{-1}}} } \; \bigstar$

$\rule{200}2$

[ 4 ]

In order to compare the speeds, we need to convert both speeds into same units.

• First speed = 24 km/h
• Second speed = 12.8 m/s

Let's convert both speed in m/s. First one is already in km/h. We have to convert second one in m/s.

⇒ Second speed = 12.8 m/s

⇒ Second speed = (12.8 × 18/5) km/h

⇒ Second speed = (2.56 × 18) km/h

⇒ Second speed = 46.08 km/h

We get that :

First Speed > Second speed

So, a speed of 12.8 m/s is greater.

$\rule{200}2$

Given that,

• Distance = 1710 m
• Time = 3 minutes

Converting distance into km :

⇒ Distance = 1710 m

⇒ Distance = (1710 ÷ 1000) km

⇒ Distance = 1.71 km

Converting time into hours :

⇒ Time = 3 minutes

⇒ Time = (3 ÷ 60) hours

⇒ Time = 1/20 hours

Now, we'll find speed.

★ Speed = Distance ÷ Time

⇒ Speed = 1.71 km ÷ 1/20 h

⇒ Speed = (1.71 × 20) km/h

⇒ Speed = 34.2 km/h

Therefore, speed in km/h is 34.2 km/h.