Question

1 point 9. Starting from rest a train attains a velocity of 72 km per hour in 3 minutes. Its acceleration will be * O 0.9 metre per second square O 1.1 metre per second square O 0.11 metre per second square 1.9 metre per second square​

Answer 1

Provided that:

• Initial velocity = 0 mps
• Final velocity = 72 kmph
• Time = 3 minutes

To calculate:

• Acceleration

Solution:

• Acceleration = 0.11 mps sq.

Knowledge required:

• SI unit of acceleration = m/s²
• SI unit of velocity = m/s
• SI unit of time = second

Using concepts:

• We can use either acceleration formula or first equation of motion to solve this question.

• Formula to convert kmph-mps.

• Formula to convert min-sec.

Using formulas:

• Formula to convert kmph-mps:

• 1 kmph = 5/18 mps

• First equation of motion:

• v = u + at

• Acceleration formula:

• a = (v-u)/t

• Formula to convert min-sec:

• 1 min = 60 seconds

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

Required solution:

~ Firstly let us convert kmph-mps!

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

~ Now let us convert min-sec!

$:\implies \sf 1 \: min \: = 60 \: seconds \\ \\ :\implies \sf 3 \: minutes \: = 3 \times 60 \: seconds \\ \\ :\implies \sf 3 \: minutes \: = 180 \: seconds \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

~ Now let us find out the acceleration!

By using acceleration formula...

$:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-0}{180} \\ \\ :\implies \sf a \: = \dfrac{20}{180} \\ \\ :\implies \sf a \: = \dfrac{2}{18} \\ \\ :\implies \sf a \: = \dfrac{1}{9} \\ \\ :\implies \sf a \: = 0.11 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 0.11 \: ms^{-2}$

By using first equation of motion...

$:\implies \sf v = u + at \\ \\ :\implies \sf 20 = 0 + a(180) \\ \\ :\implies \sf 20 - 0 = 180a \\ \\ :\implies \sf a \: = \dfrac{20}{180} \\ \\ :\implies \sf a \: = \dfrac{2}{18} \\ \\ :\implies \sf a \: = \dfrac{1}{9} \\ \\ :\implies \sf a \: = 0.11 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 0.11 \: ms^{-2}$

• Henceforth, acceleration = 0.11 metre per second sq. Henceforth, option (c) is correct!