Question

A train starts from rest and accelerates uniformly at the rate of 5 m/s2for 5 sec. Calculate the velocity of the train and the distance covered by the train after 5 sec.

Answer 1

Refer to the attachment!!

Answer 2

Given :-

• Acceleration of the train = 5 m/s²
• Time taken = 5 seconds

To Find :-

• Velocity of the train
• Distance covered by the train

Formula used :-

$\bf \longrightarrow\red { v = u + at} \: (First \: equation \: of \: motion) \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf \longrightarrow\pink{s = ut + \frac{1}{2} a {t}^{2} } \: ( Second \: equation \: of \: motion)$

Where,

• v = final velocity
• u = initial velocity
• t = time taken
• s = distance covered
• a = acceleration

First of all, we will find velocity of the train,

$\longrightarrow \sf \: v = u + at \\ \longrightarrow \sf \: 0 + 5 \times 5 \: \: \\\longrightarrow \sf v = 25 \: m/ {s}$

Now, for the distance,

$\sf \longrightarrow \: ut + \frac{1}{2} a {t}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \: 0 \times 5 + \frac{1}{2} \times 5 \times {5}^{2} \\ \sf \longrightarrow \: \frac{1}{2} \times {5}^{3} = \frac{1}{2} \times 125 \:\\ \sf \longrightarrow \frac{1}{ \cancel2} \times \cancel{125} = 62.5 \: m \: \:$

$\sf\red {\therefore velocity = 25 m/s} \: \: \: \\ \sf \pink {and \: distance = 62.5 m}$

$✯ \: \bf \underline {Important : - }$

There are three equations of motion :-

$\bf \longrightarrow\red { v = u + at} \: (First \: equation \: of \: motion) \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf \longrightarrow\pink{s = ut + \frac{1}{2} a {t}^{2} } \: ( Second \: equation \: of \: motion) \\ \bf \longrightarrow\blue {{v}^{2} = {u}^{2} + 2as} \: ( Third \: equation \: of \: motion) \:$

$\sf{↦ First \: equation \: of \: motion \: is \: also \: known \: as \: " Velocity - time \: relation" } \: \: \: \: \: \: \\ \sf↦Second \: equation \: of \: motion \: is \: also \: known \: as \: " \: position - time \: relation". \\ \sf↦Third \: equation \: of \: motion \: is \: also \: known \: as \: "velocity - position \: relation"$