Question

An object of mass m and velocity v has kinetic energy 900J. Find the new kinetic energy if the velocity of the object becomes one - third?

Answer 1

Kinetic Energy (KE) = 1/2 mv^2
So..KE varies as v^2
Therefore if velocity becomes 1/3 times.. The KE will become (1/3)^2= 1/9 times i.e. 900J x 1/9 =100J

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{New\:kinetic\:energy=100\:J}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Mass \: of \: object = m \\ \\ \tt: \implies Kinetic \: energy(K.E) = 900 \: joule\\\\ \tt:\implies Velocity\:of\:object\:=v \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies New \: kinetic\: energy= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Kinetic \: energy = \frac{1}{2} m {v}^{2} \\ \\ \tt: \implies 900 = \frac{1}{2} \times m \times {v}^{2} \\\\ \tt:\implies 1800=mv^{2}-----(1)$

$\tt \circ \: Velocity= \frac{v}{3}\: m/s \\ \\ \bold{For \: new \: kinetic \: energy} \\ \tt: \implies K.E = \frac{1}{2} \times m \times {(\frac{v}{3})}^{2} \\ \\ \tt: \implies 18K.E= m {v}^{2} - - - - - (2) \\ \\ \text{Putting \: value \: of \: mv}^{2} \text{ \: in \: (2)}\\\\ \tt:\implies 18K.E=1800 \\ \\ \green{ \tt: \implies K.E = 100 \:J} \\ \\ \green{\tt \therefore New \: kinetic \:energy \: is \: 100 \: J}$