Question

Find the chance in kinetic energy if a body having mass 30 kg descends its speed from 20 m/s to 15 m/s.​

Answer 1

Given :

• Mass of a body = 30 kg
• Initial speed of a body = 20 m/s
• Final speed of a body = 15 m/s

To Find :

• The change in kinetic energy of the body

Solution :

The Kinetic energy of a body is given by ,

$\\ \star \: {\boxed{\purple{\sf{KE = \dfrac{1}{2}m {v}^{2} }}}}$

First let us calculate the initial kinetic energy of the body . we have ,

• m = 30 kg
• u = 20 m/s

$\\ : \implies \sf \:KE_{i} = \dfrac{1}{2} \times 30 \times {(20)}^{2}$

$\\ : \implies \sf \: KE_{i} = 15 \times {(20)}^{2}$

$\\ : \implies \sf \: KE_{i} = 15 \times 400$

$\\ : \implies{\underline{\boxed{\red{\mathfrak{KE_{i} = 6000 \: J}}}}}$

So , The initial kinetic energy of the body is 6000 J.

Now , Let us calculate the Final kinetic energy of the body. We have ,

• m = 30 kg
• v = 15 m/s

$\\ : \implies \sf \:KE_{f} = \dfrac{1}{2} \times 30 \times {(15)}^{2}$

$\\ : \implies \sf \: KE_{f} = 15 \times {(15)}^{2}$

$\\ : \implies \sf \: KE_{f} = 15 \times 225$

$\\ : \implies{\underline{\boxed{\red{\mathfrak{KE_{f} = 3375 \: J}}}}}$

Now , Calculating the change in kinetic energy ;

$\\ : \implies \sf \Delta \: KE = KE_{f} - KE_{i}$

$\\ : \implies \sf \Delta \: KE = 3375 - 6000$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak {\Delta \:KE = - 2625 \: J}}}}} \: \bigstar$

Hence ,

• The Change in kinetic energy of the given body is 2625 J.

Answer 2

Answer:

Given :-

• Mass of body (M) = 30 kg
• Initial velocity (U) = 20 m/s
• Final velocity (V) = 15 m/s

To Find :-

Change in kinetic energy

Solution :-

As we know that

$\huge \mathrm {KE \: = \dfrac{1}{2} m {v}^{2} }$

Let's find the initial kinetic energy

$\sf {KE}_{i} = \dfrac{1}{2} \times m \: u {}^{2}$

$\sf \: KEi \: = \dfrac{1}{2} \times 30 \times {20}^{2}$

$\sf \: KEi \: = 1 \times 15 \times 400$

$\sf \: KEi \: = 6000 \: J$

Now,

Let's find final kinetic energy

$\sf \: KEf \: = \dfrac{1}{2} \times mv {}^{2}$

$\sf \: KEf \: = \dfrac{1}{2} \times 30 \times {15}^{2}$

$\sf \: KEf \: = 1 \times 15 \times 225$

$\sf \: KEf \: = 15 \times 225$

$\sf \: KEf = 3375$

Now,

Let's find the change in kinetic energy

$\sf \: change \: in \: KE = KEf - KEi$

$\sf \triangle \: KE = 3375 - 6000$

$\sf \triangle \: KE = - 2625 \: J$