Question

A mass of 2 kg at rest travels for 4 sec with an acceleration of 2.5 ms^-2. The gain in its momentum is (in kg ms^-1)

Answer 1

Explanation:

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Answer is 20.

Answer 2

Provided that:

• Mass = 2 kg
• Initial velocity = 0 mps
• Time = 4 seconds
• Acceleration = 2.5 m/s sq.

Don't be confused! Initial velocity cames as zero because the body is initially at rest.

To calculate:

• The gain in momentum

Solution:

• The gain in momentum = 20 kilograms metre per second

Using concepts:

• Momentum formula
• First equation of motion

Using formulas:

• Momentum formula:

• ${\small{\underline{\boxed{\pmb{\sf{p \: = mv}}}}}}$

• First equation of motion:

• ${\small{\underline{\boxed{\pmb{\sf{v \: = u \: + at}}}}}}$

Where, v denotes final velocity, u denotes initial velocity, a denotes acceleration, t denotes time taken, m denotes mass and p denotes momentum.

Required solution:

~ Firstly calculating initial momentum by using suitable formula!

→ Momentum = Mass × Velocity

→ p = mu

→ p = 2(0)

→ p = 0 kg m/s

→ Initial momentum = 0 kg m/s

~ Now solve this question there is a need to find out the final velocity, let's calculate final velocity by using first equation of motion!

→ v = u + at

→ v = 0 + 2.5(4)

→ v = 0 + 10.0

→ v = 10 m/s

→ Final velocity = 10 m/s

~ Now calculating final velocity by using suitable formula!

→ Momentum = Mass × Velocity

→ p = mv

→ p = 2(10)

→ p = 20 kg m/s

→ Final momentum = 20 kg m/s

~ Now let's see what is gain in momentum!

→ Gain in momentum = Final momentum - Initial momentum

→ Gain in momentum = 20 - 0

→ Gain in momentum = 20 kg m/s