Question

A train travelling at 36 km/h and accelerate uniformly at 2 m/s² calculate its velocity after 5 seconds.​

Answer 1

Provided that:

• Initial velocity = 36 km/h
• Acceleration = 2 m/s²
• Time taken = 5 seconds

To calculate:

• Final velocity

Solution:

• Final velocity = 20 m/s

Using concepts:

• Formula to convert kmph-mps

• Formula to find acceleration to calculate the final velocity.

• Or except of acceleration formula we can use the mentioned equation to calculate the final velocity too.

• First equation of motion

Using formulas:

${\small{\underline{\boxed{\sf{Kmph \: = \dfrac{5}{18} \: mps}}}}}$

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

• And first equation of motion,

${\small{\underline{\boxed{\sf{v \: = u \: + at}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity, t denotes time taken, kmph denotes kilometre per hour and mps denotes metre per second

Required solution:

~ Firstly let us convert kmph-mps!

$:\implies \sf 36 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{36} \times \dfrac{5}{\cancel{{18}}} \: (Cancelling) \\ \\ :\implies \sf 2 \times 5 \\ \\ :\implies \sf 10 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

~ Now let's calculate the final velocity!

Using acceleration formula!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf 2 \: = \dfrac{v-10}{5} \\ \\ :\implies \sf 2 \times 5 \: = v - 10 \\ \\ :\implies \sf 10 \: = v - 10 \\ \\ :\implies \sf 10 + 10 \: = v \\ \\ :\implies \sf 20 \: = v \\ \\ :\implies \sf v \: = 20 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 20 \: ms^{-1}$

Using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf v \: = 10 + 2(5) \\ \\ :\implies \sf v \: = 10 + 10 \\ \\ :\implies \sf v \: = 20 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 20 \: ms^{-1}$

Answer 2

Answer:-

• Initial velocity=u=36km/h

Convert it to m/s

$\\ \sf\Rrightarrow 36\times \dfrac{5}{18}$

$\\ \sf\Rrightarrow 2\times 5$

$\\ \sf\Rrightarrow 10m/s$

• Time=t=5s
• Acceleration=a=2m/s^2[/tex]
• Final velocity=v=?

According to first equation of motion

$\\ \sf\Rrightarrow v=u+at$

$\\ \sf\Rrightarrow v=10+2(5)$

$\\ \sf\Rrightarrow v=10+10$

$\\ \sf\Rrightarrow v=20m/s$