Question

a train starting from rest travels with uniform acceleration and acquires a velocity of 80 kilometre in 2 minutes find the acceleration and distance travelled by the train this time​

Answer 1

Given :-

Initial. velocity of train (u) =0 [ start from rest ]

final velocity of train (v) =80km/h

Time (t) =2 minutes

To find:-

The acceleration and distance travelled by train in the given time

• By first equation of motion we can find the acceleration of train

$\bigstar{\boxed{\textsf {\textbf {v=u+at}}}}$

• Convert given velocity and time in SI units

$\longmapsto\sf 80\times \dfrac{5}{18} =\cancel{\dfrac{400}{18}}\\ \\ \longmapsto\sf v =22.22m/s\\ \\ \longmapsto\sf Time = 2 min \\ \\ \longmapsto \sf 2\times 60 = 120 seconds$

• find the Acceleration !

$\longmapsto\sf 22.22= 0+ a\times 120\\ \\ \longmapsto\sf \cancel{\dfrac{22.22}{120}}=a\\ \\ \longmapsto\sf a=0.185m/s^2$

$\bigstar{\boxed{\textsf {\textbf {Acceleration (a)= 0.185m/s}}^2}}$

• Find the distance

$\bigstar{\boxed{\sf{s=ut+\dfrac{1}{2}at^2}}}$

$\longmapsto\sf s = 0\times 120+ \dfrac{1}{\cancel2}\times 0.185\times \cancel{120}\times 120\\ \\ \longmapsto\sf s= 0+ 0.185\times 60\times 120\\ \\ \longmapsto\sf s= 1332 m$

$\bigstar{\boxed{\textsf {\textbf {Distance \ covered (s)= 1332m}}}}$

Answer 2

$\Large\displaystyle{\underline{\tt{GIVEN:-}}}$

A train starting from rest travels with uniform acceleration and acquires a velocity of 80 km/h in 2 minutes.

• Initial velocity, u = 0 km/h

• Final velocity, v = 80 km/h = 22.22 m/s

• Time, t = 2 minutes = 120 s

$\Large\displaystyle{\underline{\tt{TO\ DETERMINE:-}}}$

The acceleration and distance travelled by the train in this time​.

$\Large\displaystyle{\underline{\tt{ACKNOWLEDGEMENT:-}}}$

We must know,

• v = u + at

• s = ut + 1/2 at²

$\Large\displaystyle{\underline{\tt{ANSWER:-}}}$

Putting the values in the first equation :-

22.22 = 0 + a(120)

⇒22.22 = 120a

⇒a = 22.22/120

⇒a = 0.185 m/s²

$\rule{146}{2}$

Now,

Again, putting all the known values in the second equation above :-

s = 0(120) + 1/2 × 0.185 × (120)²

⇒s = 0 + 0.0925 × 14400

⇒s = 1332 m   or   1 km 332 m