Question

1. How much time will a 500 m long train take to cross a tree if it is moving at a speed of 72 km/h?
(Hint: Take the length of the train as the distance.)​

Answer 1

Given -

• Length of train is 500m

• velocity of train is 72km/hr

To find -

• How much time will it take to cross the tree.

Formula used -

$\sf \: time \: = \dfrac{distance}{speed}$

Solution -

In the question, we are provided with the length of train and it's speed, and we need to find the time it will take to cross the tree. As we can see that the velocity is given in km/hr, so first we will covert it into m/s, then we will put the formula of time = Distance/speed, which will give us the time. Let's do it!

According to question -

$\sf Length_{(of\:train)}\:=\: 500\:m$

$\sf velocity_{(of\:train)}\: =\: 72\:km/hr$

$\sf \: velocity_{(of\:train)} \: = 72 \: \times \dfrac{5}{18}$

$\sf \: velocity_{(of\:train)} \: = 20 \: m/s$

Now -

We will first give the actual formula, that is, distance = speed × time , then we will give the formula by which, the above question will be done.

$\sf \: distance = speed \: \times \: time$

After interchanging distance with time -

$\sf \: time = \dfrac{distance}{speed}$

$\sf \: time = \dfrac{500}{20}$

$\sf \: time = 25 \: s$

$\therefore$ The train will take 25 seconds to cross the tree.

______________________________________________

Answer 2

${\large{\bold{\rm{\underline{Let's \; understand \; the \; concept \: 1^{st}}}}}}$

★ This question says that we have to find out the time in which the 500 metres long train take to cross a tree if it is moving at a speed of 72 km/h? There is a hint given for us and the hint is that we have to take the length of the train as the distance. So, it's clear to us that we have to use the formula to find out the time here because it's asked here !

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Train is moving at a speed of 72 km/h

★ Length of the train = 500 m

$\; \; \; \; \; \; \; \; \;{\bold{\tt{According \; to \; the \; given \; hint}}}$

* The length of the train is the distance !

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Time will which the given train cross the tree.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Time will which the given train cross the tree = ${\sf{\bold{\red{25 \: seconds}}}}$

${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

★ Formula to find time.

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

${\sf{\rightarrow Time \: = \: \dfrac{Distance}{Speed}}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

✨ Firstly let us convert km/h into m/s. Because the distance is given in metres but the speed is given in km/h so there is a need to convert them !....

According to the question,

⚕️ Length = 500 m

⚕️ Speed = 72 km/h

⚕️ Speed = 72 × ${\sf{\dfrac{5}{18}}}$

⚕️ Speed = 4 × 5

⚕️ Speed = 20 m/s

Now let's find time -

⚕️ ${\sf{Time \: = \: \dfrac{Distance}{Speed}}}$

⚕️ ${\sf{Time \: = \: \dfrac{500}{20}}}$

⚕️ ${\sf{Time \: = \: \dfrac{50}{2}}}$

⚕️ ${\sf{Time \: = 25 \: seconds}}$

$\; \; \; \; \; \;{\small{\boxed{\boxed{\bf{25 \: seconds \: is \; time \: taken \: by \: train \: to \: cross \: tree}}}}}$