Question

Find the change of momentum of a car in S.I. unit if its velocity increases from 36 km/hr to 144 km/hr in 5 s.( mass of the car is 1000 kg). Here the car is moving in the same direction.​

Answer 1

Provided that:

• Initial velocity = 36 kmph
• Final velocity = 144 kmph
• Time = 5 seconds
• Mass = 1000 kg

To calculate:

• Change in momentum

Solution: 3,00,00,000 kg mps or 3 × 10⁷ kg mps is the change in momentum.

Using concepts:

• Formula to convert kmph-mps
• Initial momentum formula
• Final momentum formula
• Change in momentum formula

Using formulas:

• 1 kmph = 5/18 mps
• p = mu
• p′ = mv
• ∆p = m(v-u)

Where, p denotes initial momentum, m denotes mass, u denotes initial velocity, v denotes final velocity, p′ denotes final momentum and ∆p denotes change in momentum.

Required solution:

~ Firstly let us convert kmph-mps!

Converting 36 kmph-mps!

→ 1 kmph = 5/18 mps

→ 36 kmph = 36 × 5/18 mps

→ 36 kmph = 2 × 5 mps

→ 36 kmph = 10 mps

• Henceforth, converted!

Now converting 144 kmph-mps!

→ 1 kmph = 5/18 mps

→ 144 kmph = 144 × 5/18 mps

→ 144 kmph = 8 × 5 mps

→ 144 kmph = 40 mps

• Henceforth, converted!

~ Now let us find the out initial momentum!

→ p = mu

→ p = 1000(10)

→ p = 10000 kg mps

• Henceforth, founded!

~ Now let us find the out final momentum!

→ p′ = mv

→ p′ = 1000(40)

→ p′ = 40000 kg mps

• Henceforth, founded!

~ Now let us find out the change in momentum!

→ ∆p = m(v-u)

→ ∆p = 1000(40000-10000)

→ ∆p = 1000(30000)

→ ∆p = 3,00,00,000 kg mps $\:$

→ ∆p = 3 × 10⁷ kg mps

Answer 2

GIVEN:-

• Initial velocity(u)=36 km/hr==>36×5/18=10 m/s
• Final velocity=(v)=144 km/hr==>144×5/18=16 m/s

• Time=5 second
• Mass=1000 kg

TO FIND :-

change in momentum

EXPLANATION:-

We know that:-

F=Δp/t   (newton's 2nd law)

Δp=F×t

So the find change in momentum ,we have to find the product of force acting and time,

Time= 5 s

F= ?

We know that×,

F=ma

M=1000

a=(v-u)/t

v=16 m/s

u=10 m/s

t=5 second

a=(16-10)/5

a=6/5 m/s²

Now,

F=ma

F=1000×6/5

F=1200 N

Now ,we know F and time so we can calculate change in momentum,

Δp=F×t

Δp=1200×5

ΔP=6000 N/s

So the change in momentum is 6000 N/s