Question

A train accelerates from 18 km/h to 72 km/h in 15 sec. Find its acceleration​

Answer 1

Provided that:

• Initial velocity = 18 km/h
• Final velocity = 72 km/h
• Time taken = 15 seconds

To calculate:

• The acceleration

Solution:

• The acceleration = 1 mps sq.

Using concepts:

• Acceleration formula
• Formula to convert kmph-mps

Using formulas:

• Acceleration is given by,

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity, t denotes time taken.

• Formula to convert kmph-mps:

• ${\small{\underline{\boxed{\sf{1 \: kmph \: = \dfrac{5}{18} \: mps}}}}}$

Required solution:

~ Firstly let us convert initial velocity into metre per second!

$\begin{gathered}:\implies \sf 18 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{18} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 1 \times 5 \\ \\ :\implies \sf 5 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}\end{gathered}$

~ Now let us convert final velocity into metre per second!

$\begin{gathered}:\implies \sf 72 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{72} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 4 \times 5 \\ \\ :\implies \sf 20 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}\end{gathered}$

Therefore,

• Initial velocity is 5 m/s
• Final velocity is 20 m/s

~ Now let's calculate acceleration!

$\begin{gathered}:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Change \: in \: time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-5}{15} \\ \\ :\implies \sf a \: = \dfrac{15}{15} \\ \\ :\implies \sf a \: = \cancel{\dfrac{15}{15}} \\ \\ :\implies \sf a \: = 1 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 1 \: ms^{-2}\end{gathered}$

Answer 2

Given :

Initial velocity of the train : 18 km/hr

Final velocity of the train : 72 km/hr

Time taken : 15 sec

To find :

The acceleration of the train.

Solution :

Firstly we have to convert km/hr to m/s

we know that,

» 1km/hr = 5/18km/hr

» 18km/hr = 18 × 5/18 = 5 m/s

» 72km/hr = 72 × 5/18 = 20 m/s

Accerlation is the rate of change of velocity.

• It is a vector quantity having both magnitude as well as direction.
• SI unit of acceleration is metre per second square.

As we are provided with initial velocity, final velocity and time we can use first equation of kinematics that is,

v = u + at

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time taken

by substituting all the given values in the formula,

➝ v = u + at

➝ 20 = 5 + a(15)

➝ 15a = 20 - 5

➝ 15a = 15

➝ a = 15/15

➝ a = 1 m/s²

Thus, the acceleration of the train is 1 m/s².

$\:$

Know more :

First equation of kinematics : v = u + at

Second equation of kinematics : s = ut + 1/2at²

Third equation of kinematics : v² - u² = 2as