Question

A motorcycle moving with the speed of 5m/s is subjected to an acceleration of 0.2m/s^2. Calculate the speed of the motorcycle after 10 seconds , and the distance travelled in this time

Answer 1

GIVEN:-

• $\rm{Initial\:Velocity=5m/s}$

• $\rm{Acceleration=0.2m/s^{2}}$

• $\rm{Time=10s}$

TO FIND:-

• The speed of the motorcycle after 10 Second and the distance travelled in this time.

FORMULAE USED:-

• ${\huge{\boxed{\rm{v=u+at}}}}$

Where,

V= Final Velocity

u= initial Velocity

a= Acceleration

t= Time

• ${\huge{\boxed{\rm{v^{2}-u^{2}=2as}}}}$

Where,

V= Final Velocity

u= initial Velocity

a= Acceleration

S= Distance.

Now,

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

$\implies\rm{v=5+0.2\times{10}}$

$\implies\rm{v=5+\dfrac{2}{\cancel{10}}\times{\cancel{10}}}$

$\implies\rm{v=7m/s}$

Thus, The final Velocity is 7m/s^-1

Now,

$\implies\rm{v^2-u^2=2as}$

$\implies\rm{(7)^2-(5)^2=2\times{0.2}\times{s}}$

$\implies\rm{49-25=\dfrac{2}{5}\times{s}}$

$\implies\rm{24\times{5}=2s}$

$\implies\rm{120=2s}$

$\implies\rm{s=\dfrac{\cancel{120}}{\cancel{2}}}$

$\implies\rm{S= 60m}$

Thus, The distance travelled by Motorcycle is 60m

Answer 2

Given

$\bf \red{ Initial \: Velocity \: (u) = 5 \: m \: {s}^{ - 1} }$

$\bf \red{ Acceleration \: (a) = 0.2 \: m \: {s}^{-2} }$

$\bf \red{ Time \: (t) = 10 \: s }$

Calculating Final Velocity of the Motorcycle

As, we know

$\huge \boxed{ \boxed{ \bf \: v = u + at }}$

Substituting the Values

$\longrightarrow \bf v = 5 + 0.2 \times 10$

$\longrightarrow \bf v = 5 + \dfrac{2}{ \cancel{10}} \times \cancel{ 10}$

$\longrightarrow \bf v = 5 + 2$

$\longrightarrow \bf v = 7 \: m \: {s}^{ - 1}$

Thus, the Final Velocity (v) of the MotherCycle is $\bf 7 \: m \: {s}^{ - 1}$

Calculating, Distance Travelled

As, we know

$\huge \boxed{ \boxed{ \bf {v}^{2} - {u}^{2} = 2as }}$

Substituting the Values

$\longrightarrow \bf( {7}^{2} ) - ( {5}^{2} ) = 2 \times 0.2 \times s$

$\longrightarrow \bf49 - 25 = 2 \times \dfrac{2}{10} \times s$

$\longrightarrow \bf24 = \dfrac{2}{5} s$

$\longrightarrow \bf 24 \times 5 = 2s$

$\longrightarrow \bf 120 = 2s$

$\longrightarrow \bf 2s = 120$

$\longrightarrow \bf s = \cancel{\dfrac{120}{2} }$

$\longrightarrow \bf s = 60 \: m$

Thus, Distance Travelled by MotherCycle is $\bf 60 \: m$

Hence

$\bf Final \: Velocity \: (u) = 7 \: m \: {s}^{ - 1}$

$\bf Distance \: Travelled = 60 \: m$