Question

a bus starting from rest and moving with uniform acceleration attains a speed of 30m/s in 2 minutes. the displacement of the bus is​

Answer 1

To find displacement, at first we have to find the acceleration. So let's start:

Calculating Acceleration

We have,

Initial velocity (u) = 0 m/s

Final velocity (v) = 30 m/s

Time (t) = 2min = 120s [ 1m = 60s]

Acceleration (a) = ???

Using 1st equation of motion, we have,

v = u + at

$⟹0=30+a×120$

$⟹30+a×120=0$

$⟹a×120=-30$

$⟹a=\frac{-30}{120}$

$⟹a=-\frac{1}{4}$

$⟹a=-0.25$ [Retardation(-)]

Calculating Displacement

We have,

Initial velocity (u) = 30 m/s

Time (t) = 2min = 120s

Acceleration (a) = -0.25 [Retardation(-)]

Using second equation of motion, we have,

$\pink{\underline{\underline{\frak{s=ut+\frac{1}{2}at^2}}}}$

$\sf\implies{s=30×120+\frac{1}{2}×(-0.25)×120^2}$

$\sf\implies{s=3600+\frac{1}{2}×(-0.25)×120^2}$

$\sf\implies{s=3600+\frac{1}{2}×(-3600)}$

$\sf\implies{s=3600+(-1800)}$

$\sf\implies{s=3600-1800)}$

$\sf\implies{s=1800m}$ (Required Answer)

Therefore, displacement of the bus is 1800m

Answer 2

To find displacement, at first we have to find the acceleration. So let's start:

Calculating Acceleration

We have ,

Initial velocity (u) = 0 m/s

Final velocity (v) = 30 m/s

Time (t) = 2min = 120s [ 1m = 60s]

Acceleration (a) = ???

Using 1st equation of motion , we have ,

v = u + at

$⟹ 0=30+a×120 \\ ⟹30+a×120=0 \\ ⟹a×120=-30 \\ \\⟹a=\frac{-30}{120}$

$⟹a=-\frac{1}{4}$

$⟹a = −0.25 [Retardation(-)]$

Calculating Displacement

We have ,

Initial velocity (u) = 30 m/s

Time (t) = 2min = 120s

Acceleration (a) = - 0.25 [Retardation(-)]

Using second equation of motion , we have ,

$\begin{gathered}\pink{\underline{\underline{\frak{s=ut+\frac{1}{2}at^2}}}}\\\end{gathered}$

$\begin{gathered}\sf\implies{s=30×120+\frac{1}{2}×(-0.25)×120^2}\\\end{gathered}$

$\begin{gathered}\sf\implies{s=3600+\frac{1}{2}×(-0.25)×120^2}\\\end{gathered}$

$\begin{gathered\sf\implies{s=3600+\frac{1}{2}×(-3600)}\\\end{gathered}$

$\sf\implies{s=3600+(-1800)} \\ \sf\implies{s=(3600-1800)} \\ \sf\implies{s=1800m} \: \: (Required Answer)$

Therefore, displacement of the bus is 1800m