Question

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Kinetic energy of an object of mass, m moving with a velocity of 5 ms 1 is 25 What will be its kinetic energy when its velocity is doubled? What will be its kine energy when its velocity is increased three times.


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Answer 1

Answer:

Kinetic energy is 25 units.

KE is directly proportional to velocity square.

If v is doubled,KE will be quadrupled, KE will be 100 units.

If v is tripled, KE = 25* 9 = 225 units.

Explanation:

Answer 2

Given

• Kinetic energy = 25J.
• Velocity = 5m/s.
• Mass is m.

To find

• Kinetic energy when velocity is doubled. [Case 1]
• Kinetic energy when velocity is tripled. [Case 2]

Solution

In this problem we will first calculate mass from kinetic energy and velocity. After getting mass we can easily calculate kinetic energy for both the cases by substituting values. In 1st case we have to double the velocity as asked in the problem and in 2nd case we have to increase the velocity by three times as asked in the problem.

Let's start our calculations :-

Calculating Mass

K.E. = ½ mv²

Substituting values

=> 25 = ½ × m (5)²

=> 25 = ½ × m × 25

=> m = ½ × 25 × 1/25

=> m = 2kg.

Case 1

K.E. = ½ × m × (2v)² [v is doubled i.e 2v]

=> K.E. = ½ × 2 × (2×5)²

=> K.E. = ½ × 2 × (10)²

=> K.E. = ½ × 2 × 100

=> K.E. = 100J.

Case 2

K.E. = ½ × m × (3v)² [v is tripled i.e. 3v)

=> K.E. = ½ × 2 × (3×5)²

=> K.E. = ½ × 2 × (15)²

=> K.E. = ½ × 2 × 225

=> K.E. = 225J.

Final Answer

• 100J is the kinetic energy.
• 225 is the kinetic energy.

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