Question

a train travelling at a uniform speed covers a distance of 35 km between two station in 50 minutes calculate its speed in metre per second and in kilometre per hour​

Answer 1

Given :-

Distance ( D) =35Km

Time (T) =50 minutes

To find :-

The speed of train in m/s and km/s

Now :-

• First convert it into km/h

$\sf 50 \ minutes \ in \ Hour \\ \\ \sf\longrightarrow\sf \cancel{\dfrac{50}{60}}= \dfrac{5}{6} hrs$

Now find the speed of train

$\bigstar{\boxed{\sf{Speed=\dfrac{Distance }{Time }}}}$

$\longrightarrow\sf Speed= \dfrac {D}{T}\\ \\ \longrightarrow\sf Speed=\dfrac{35}{\dfrac{5}{6}}\\ \\ \longrightarrow\sf Speed = \cancel{35}\times \dfrac{6}{\cancel{5}}\\ \\ \longrightarrow\sf Speed = 7\times 6\\ \\ \longrightarrow\sf Speed = 42km/h$

• Now In m/s

$\underline{\textsf{\textbf{\dag \ \ Note :- }}}$

• To convert speed from km/h to m/s

$\sf \bullet Multiply \ with\ \ \dfrac{5}{18}$

• To convert speed from m/s to km/h

$\sf \bullet Multiply \ with\ \ \dfrac{18}{5}$

$\sf \ \ we \ have\ \ 42 \ km/h\\ \\ \sf \ \ \ Convert \ in \ m/s\\ \\ \longrightarrow \sf 42\times \dfrac{5}{18}\\ \\ \longrightarrow\sf \dfrac{ 42\times 5}{18}\\ \\ \longrightarrow\sf \cancel{\dfrac{210}{18}}\\ \\ \longrightarrow\sf 11.67m/s$

$\boxed{\sf { Speed \ of \ Train \ in \ km/h =42km/h}}$

$\boxed{\sf { Speed \ in \ m/s = 11.67m/s}}$

Answer 2

Given

Distance travelled by train = 35 km.

Time taken by train = 50 minutes.

To find

Speed of train in km/h & m/s

Solution

Here distance travelled by train = 35 km.

Time = 50 minutes.

➪ Time = (50/60) hours

➪ Time (t) = 5/6 hours.

We know that,

$\longrightarrow\underline{\boxed{\sf\blue{Speed = \dfrac{Distance(d)}{Time(t)} }}}\: \star \\\\\longrightarrow\sf Speed = \dfrac{35}{\dfrac{5}{6}} \\\\\longrightarrow\sf Speed = \cancel{35} \times \dfrac{6}{\cancel{5}} \\\\\longrightarrow\sf Speed = 7 \times 6 \\\\\longrightarrow\underline{\boxed{\textsf{\textbf{Speed = 42 km/h }}}}\\\\\\\therefore\underline{\textsf{Speed of train = {\textbf{42 km/h }}}}$

$\rule{200}{1}$

Again, distance travelled by train = 35 km = 35 × 1000 = 35000 m

Time taken = 5/6 h = (5/6) × 3600 = 3000 s

Using the speed formula :

$\longrightarrow\sf Speed = \dfrac{35000}{3000} \\\\\longrightarrow\underline{\boxed{\textsf{\textbf{Speed = 11.67 m/s }}}}\\\\\\\therefore\underline{\textsf{Speed of train = {\textbf{11.67 m/s }}}}$