Question

An object of mass 100kg is accelerated uniformly from 4m/s to 8m/s in 5s. find its initial momentum, final momentum, and the change in momentum.
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Answer 1

Given:-

• Maas of object ,m = 100kg

• Initial velocity ,u = 4m/s

• Final velocity ,v = 8m/s

• Time taken ,t = 5s

To Find:-

• Initial momentum ,pi

• Final momentum , pf

• Change in Momentum, p

Solution:-

Initial Momentum

• pi = mu

Substitute the value we get

→ pi = 100×4

→ pi = 400kgm/s

Therefore, the initial momentum of the object is 400kgm/s.

Final Momentum

•pf = mv

Substitute the value we get

→ pf = 100×8

→ pf = 800kgm/s

Therefore, the final momentum is 800kgm/s.

Rate of Change Of Momentum

•p = pf -pi/t

Substitute the value we get

→ p = 800-400/5

→ p = 400/5

→ p = 80kgm/s

Therefore , the rate of change of momentum is 80kgm/s.

Answer 2

Answer:

Given :-

• An object of mass 100 kg is accelerated uniformly from 4 m/s to 8 m/s in 5 secs.

To Find :-

• What is the value of initial momentum, final momentum and the change in momentum.

Formula Used :-

For initial momentum,

$\boxed{\bold{\large{ρi\: = mu}}}$

For final momentum,

$\boxed{\bold{\large{ρf\: =\: mv}}}$

For change in momentum,

$\boxed{\bold{\large{ρ\: =\: ρf\: -\: \dfrac{ρi}{t}}}}$

Solution :-

• m = 100 kg
• u = 4 m/s
• v = 8 m/s
• t = 5 secs

According to the question by using the following formula we get,

❶ Initial momentum,

⇒ ρi = 100 × 4

⇒ ρi = 400 kgm/s

$\therefore$ The initial momentum of an object is 400 kgm/s .

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❷ Final momentum,

⇒ ρf = 100 × 8

⇒ ρf = 800 kgm/s

$\therefore$ The final momentum of an object is 800 kgm/s .

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❸ Change in momentum,

⇒ ρ = 800 - $\dfrac{400}{5}$

⇒ ρ = $\dfrac{400}{5}$

⇒ ρ = 80 kgm/s

$\therefore$ The change in momentum of an object is 80 kgm/s .

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