Question

A stone of mass 2 kg is changing its velocity from 3 m/s to 18 m/s in 15 s. The change
in KE, power delivered and force acted on the stone
(1) 300J, 20 watt, 20N
(2) 30J, 20 watt, 200N
(3) 3150, 21 Watt, 2N
(4) 330J, 21 Watt, 20N​

Answer 1

AnswEr :-

• (3) 315 J, 21 Watt, 2 N

GivEn :-

• A stone of mass 2 kg is changing its velocity from 3 m/s to 18 m/s in 15 s.

To Find :-

• The change in KE
• Power delivered
• Force acted

Solution :-

First Solution :-

The Change in KE,

$\implies \sf \: \dfrac{1}{2} m(v_{2}^{2} - v_{1} ^{2} )$

• m = mass of the object
• v2 = final velocity
• v1 = initial velocity

➠ Substituting the values,

$\implies \sf \: \dfrac{1}{2} \times 2( {18}^{2} - {3}^{2} )$

$\implies \sf \: 324 - 9$

$\implies \sf \boxed{ \red{ \bold{KE_{change} = 315 \: J}}}$

Second Solution :-

$\implies \boxed{ \sf \: P = \dfrac{E}{t} }$

• P = Power
• E = Energy
• t = time taken

➠ Substituting the values,

$\implies \sf \: P = \dfrac{315}{15}$

$\implies \sf \boxed{ \red{ \bold{ P = 21 \: watt }}}$

Third Solution :-

$\implies \sf \: a = \dfrac{(v - u)}{t}$

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

$\implies \sf \: a = \dfrac{(18 - 3)}{15}$

$\implies \sf \: a = \dfrac{15}{15} = 1$

Now,

$\implies \boxed{ \sf \: F = ma}$

• F = Force
• m = mass
• a = acceleration

$\implies \sf \: F = 2 \times 1$

$\implies \boxed{ \red{ \bold{ F = 2 N }}}$

Answer 2

$\Huge \bf \fbox {\fbox{Answer}}$

$\Large \bf{Given:}$

$\mapsto \sf{Mass \: of \: stone=2kg }$

$\mapsto \sf{Initial \: velocity \: of \: stone=3m/s}$

$\sf{ \mapsto{Final \: velocity \: of \: stone=18m/s}}$

$\sf{ \mapsto{Time \: taken \: to \: change \: in \: velocity=15sec}}$

$\Large \bf{To \: find:}$

$\leadsto \sf{Change \: in \: kinetic \: energy.}$

$\leadsto \sf{Power \: delivered \: in \: stone.}$

$\leadsto \sf{Force \: acted \: on \: the \: stone.}$

$\Large \bf{Formula \: required:}$

$\boxed{ \sf{Change \: in \: kinetic \: energy(K.E.)= \frac{1}{2}mass(change \: in \: velocity)= \frac{1}{2} m( {v_2}^{2} - {v_1}^{2} )}}$

$\boxed {\sf{Power(P)= \frac{Energy(E)}{time \: taken(t)} }}$

$\boxed {\sf{Force(F) = mass(m) \times acceleration(a)}}$

$\Large \bf{According \: to \: Question:}$

$\bf{\implies{Change \: in \: kinetic \: energy(K.E.)= \frac{1}{2}mass(change \: in \: velocity)= \frac{1}{2} m( {v_2}^{2} - {v_1}^{2} )}}$

$\sf{\implies{Change \: in \: kinetic \: energy(K.E.)= \frac{1}{2} \times 2( {18}^{2} - {3}^{2} )}}$

$\sf{\implies{Change \: in \: kinetic \: energy(K.E.)= \frac{1} {\cancel{2}} \times \cancel 2(324 - 9)} =315J }$

$\fbox{{Change \: in \: kinetic \: energy(K.E.)= 315J}}$

$\implies{\sf{Power(P)= \frac{Energy(E)}{time \: taken(t)} }}$

$\implies{\sf{Power(P)= \frac{315}{15} = 21watt}}$

$\fbox{{Power= 21watt}}$

$\sf{ \implies{Acceleration= \frac{v_2-v_1}{t}} = \frac{18 - 3}{15} = {\cancel\frac {15}{15}} = 1m/ {s}^{2} }$

$\sf{ \implies{Force(F) = mass(m) \times acceleration(a)}}$

$\sf{ \implies{Force(F) =2 \times 1 = 2N}}$

$\sf{ \fbox{Force(F) of \: stone \: 2N.}}$