Question

The kinetic energy possed by a car of mass 400kg at any instant is 28.8KJ.Find the velocity of the car at that instant.Now if the velocity of the car is half at any instant what will be its Kinetic energy at that instant.

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Answer 1

Given,

The kinetic energy possessed by a car of mass 400kg at any instant is 28.8KJ.

To find,

Find the velocity of the car at that instant. Now if the velocity of the car is half at any instant what will be its Kinetic energy at that instant.

Solution :

Mass of car = 400 kg

Kinetic energy = 28.8 KJ

As we know,

Kinetic energy = 1/2 mv²

⇒ 28.8 = 1/2 * 400 * v²

⇒ 28.8 = 200v²

⇒ v² = 28.8/200

⇒ v² = 0.144

⇒ v = √0.144

⇒ v = 0.38 m/s

∴ Velocity of the car at that instant = 0.38 m/s

Now velocity of car is half, so :

⇒ Velocity of car = 0.39/2 m/s

⇒ Velocity of car = 0.19 m/s

Mass of car, m = 400 kg

∴ Kinetic energy = 1/2 mv²

⇒ Kinetic energy = 1/2 * 400 * (0.19)²

⇒ Kinetic energy = 200 * 0.0361

⇒ Kinetic energy = 7.22 KJ

∴ Kinetic energy at that instant = 7.22 KJ

Answer 2

Answer:

Given :-

• Kinetic energy = 28.8 J
• Mass of car = 400 kg

To Find :-

• Velocity of car
• velocity of the car is half at any instant what will be its Kinetic energy at that instant.

Solution :-

As we know that

$\huge \bf \: KE = \frac{1}{2} mv {}^{2}$

Here,

KE = Kinetic energy

M = Mass

V = Velocity

$\sf \: 28.8 = \dfrac{1}{2} \times 400 \times {v}^{2}$

$\sf \: 28.8 = 1 \times 200 \times {v}^{2}$

$\sf \: v {}^{2} = \dfrac{28.8}{200}$

$\sf \: v {}^{2} = 0.144$

$\sf \: v = \sqrt{144}$

$\sf \: v = 0.38 mps$

Hence the velocity of car is 0.38 mps

Now,

Let's find when the velocity will be half

$\sf \: new \: velocity = \dfrac{0.38}{2}$

$\sf \: new \: velocity = \cancel \dfrac{0.38}{2}$

$\sf \: new \: velocity = 0.19 \: mps$

Now,

Let's find instant kinetic energy

$\huge \bf \: KE = \frac{1}{2} mv {}^{2}$

$\sf \: KE = \dfrac{1}{2} \times 400 \times 0.19 { }^{2}$

$\sf \: KE = \dfrac{1}{2} \times 400 \times 0.0361$

$\sf \: KE = 1 \times 200 \times 0.361$

$\sf \: KE = 7.22 \: KJ$