Question

The speed of a car weighing 1500 kg increases from 36 km/h to 72 km/h uniformly. What will be the change in momentum of the car?

(a) 15000 kg km/h

(b) 15000 kg m/s

(c) 54000 kg m/s

(d) 54000 g m/s​

Answer 1

Answer :

• The change in momentum of the car of mass 1500 Kg moving with increase in velocity from 36 km/h to 72 km/h is 15000 kg m/s.

Explanation :

Given :

• Mass of the car, m = 1500 kg
• Initial velocity of the car, u = 36 km/h or 10 m/s
• Final velocity of the car, v = 72 km/h or 20 m/s

To find :

• Change in momentum of the car, ∆p = ?

Knowledge required :

• Change in momentum of a body is difference of the final momentum and initial momentum.

Mathematically,

⠀⠀⠀⠀⠀⠀⠀⠀⠀∆p = (p' - p)⠀⠀⠀⠀⠀⠀...Eq.(i)

Where :

⠀⠀⠀⠀⠀⠀⠀⠀● ∆p = Change in momentum

⠀⠀⠀⠀⠀⠀⠀⠀● p' = Final momentum

⠀⠀⠀⠀⠀⠀⠀⠀● p = Initial momentum

We know that, Momentum is product of the mass and velocity of the body.

So,

⠀⠀⠀⠀⠀⠀⠀⠀⠀p = mv

Where :

⠀⠀⠀⠀⠀⠀⠀⠀● p = Momentum

⠀⠀⠀⠀⠀⠀⠀⠀● m = mass

⠀⠀⠀⠀⠀⠀⠀⠀● v = Velocity

Now by substituting the equation for p in the equation.(i), we get :

[Note :

• Final momentum will be the product of mass and the final velocity (i.e, p' = mv) and initial momentum will be the product of mass and initial velocity (i.e, p = mu)

• Mass will be same in both final momentum and initial momentum]

⠀=> ∆p = (p' - p)

⠀=> ∆p = (mv - mu)

⠀=> ∆p = m(v - u)

⠀⠀⠀⠀⠀∴ ∆p = m(v - u)

But the the above equation is the equation for Impulse experienced by a body.

[Hence we get a conclusion that,

• Change in momentum of a body = Impulse experienced by a body.]

Solution :

By using the equation for change in momentum and substituting the values in it, we get :

⠀=> ∆p = m(v - u)

⠀=> ∆p = 1500 × (20 - 10)

⠀=> ∆p = 1500 × 10

⠀=> ∆p = 15000

⠀⠀⠀⠀⠀∴ ∆p = 15000 m/s

Therefore,

• Change in momentum of the car, ∆p = 15000 kg m/s.

Answer 2

Answer:

$\huge \sf required \: answer$

• Mass of the car (m) = 1500 kg
• Initial velocity of the car (u) = 36 km/h
• Final velocity of the car (v) = 72 km/h

$\huge \sf \: to \: find$

Change in mounment of car (∆p)

$\huge \sf \: answer$

As we know that

$\sf \implies \triangle \: p \: = m \times (v - u)$

$\sf \implies \triangle \: p \: = 1500 \times (20 - 10)$

$\sf \implies \triangle \: p \: = 1500 \times 10$

$\sf \implies \triangle \: p \: = 15000 \: m/s$

$\bf \therefore \: option \: b \: is \: correct$

Change in mounment = 15000 m/s

Learn more

M - Mass

U - Initial velocity

V - Final Velocity

∆p - Mounmentum