Question

A train accelerates from 5.25 m/s to 27.56 m/s in 9.46 s. Find the displacement of the train.

Answer 1

Answer

Given -

$\rm u = 5.25 m/s$

$\rm v = 27.56 m/s$

$\rm t = 9.46 s$

where

$\longrightarrow$u is initial velocity.

$\longrightarrow$v is final velocity.

$\longrightarrow$t is time taken.

━━━━━━━━━━━━

To find -

Displacement $\longrightarrow$ s

━━━━━━━━━━━━

Solution -

For finding displacement we first need to find acceleration of particle -

━━━━━━━━━━━━

Calculation Acceleration -

$\longrightarrow$$\rm u = 5.25 m/s$

$\longrightarrow$$\rm v = 27.56 m/s$

$\longrightarrow$$\rm t = 9.46 s$

Substituting the value in 1st equation of motion -

$\rm v = u + at$

$\implies$$\rm 27.56 = 5.25 + 9.46a$

$\implies$$\rm 27.56 - 5.25 = 9.46a$

$\implies$$\rm 22.31 = 9.46a$

$\implies$$\rm a = \frac{22.31}{9.46}$

━━━━━━━━━━━━

Calculating distance travelled -

$\longrightarrow$$\rm u = 5.25 m/s$

$\longrightarrow$$\rm a = 2.35 m/s^2$

$\longrightarrow$$\rm t = 9.46 s$

$\rm s = ut + 1/2 at^2$

$\implies$$\rm s = 5.25 \times 9.46 + 1/2 \times 2.35 \times 9.46^2$

$\implies$$\rm s = 49.665 + 1/2 \times 2.35 \times 89.4916$

$\implies$$\rm s = 49.665 + 105.465$

$\implies$$\rm s = 155.13 m$

Distance travelled = 155.13 m

━━━━━━━━━━━━

Answer 2

$\huge\bf\mathbf\pink{An}\red{Sw}\blue{Er}$

• Formula to find displacement$\dashrightarrow$ $\large\underline\bold\red{V\: =\: u \: + at}$

$\longrightarrow$$\rm u = 5.25 m/s$

$\longrightarrow$$\rm v = 27.56 m/s$

$\longrightarrow$$\rm t = 9.46 s$

________________________________

• By using this formula : -

$\implies$$\rm v = u + at$

$\implies$$\rm 27.56 = 5.25 + 9.46a$

$\implies$$\rm 27.56 - 5.25 = 9.46a$

$\implies$$\rm 22.31 = 9.46a$

$\implies$$\rm a = \frac{22.31}{9.46}$

$\longrightarrow$$\rm u = 5.25 m/s$

$\longrightarrow$$\rm a = 2.35 m/s^2$

$\longrightarrow$$\rm t = 9.46 s$

_______________________________

$\rm s = ut + 1/2 at^2$

$\implies$$\rm s = 5.25 \times 9.46 + 1/2 \times 2.35 \times 9.46^2$

$\implies$$\rm s = 49.665 + 1/2 \times 2.35 \times 89.4916$

$\implies$$\rm s = 49.665 + 105.465$

$\implies$$\rm s = 155.13 m$

$\large\underline\bold\red{Hence,}$$\small\underline\bold\green{Displacement \: = 155.13 m}$

________________________________

$\large\underline\bold\red{Some \: important \: Formulas }$

• 1st equation formula $\implies$v=u+at

• 2nd equation formula$\implies$ s=ut+1/2at^2

• 3rd equation formula $\implies$v^2=v^2+at

• momentum$\implies$mass × velocity

• force$\implies$mass × acceleration

• acceleration$\implies$ change in velocity /time take

• speed$\implies$ distance /time

• velocity $\implies$displacement /time

________________________________