This post is to solve some *numerical problems related to momentum and impulse concepts in physics.* This set is good for students of class 9 & class 10 (covering grade 9 and grade 10 physics standards of different boards).

We will use this understanding from the *impulse momentum theorem*: **Impulse of force = change in momentum. **

Mathematically writing in an *impulse equation* or formula form it goes like this: **Ft = mv-mu **[ F= force, t = time duration, m = mass of the body. u and v are initial and final velocity respectively.]

**Momentum problems – ****solved using impulse equation** | worksheet with solution

**1 ] A car of mass 600 kg is moving at 15 m/s. Calculate its momentum.**

**Solution:**

momentum = mass x velocity = 600 kg x 15 m/s = 9000 kg m/s

**2 ] The driver accelerates gently so that a force of 30 N acts on the car for 10 seconds. Calculate the impulse of the force.**

**Solution:**

Impulse of the force = Force x time duration = 30 x 10 N s = 300 Ns.

**3 ] A car of mass 500 kg is moving at 20 m/s. Calculate its initial momentum.** **The driver accelerates gently so that a force of 50 N acts on the car for 8 seconds. Calculate the final momentum.****Solution**:

Initial momentum = mass x initial velocity = 500 x 20 kg m/s = 10000 kg m/s

Impulse of the force applied = force x time duration = 50 x 8 Ns = 400 Ns

We know that the **impulse of force = change of momentum**

The car had an acceleration, so the **final momentum = initial momentum + impulse of force = (10000 + 400) kg m/s =10400 kg m/s**

**4 ] Calculate the momentum of a car of mass 600 kg moving at 30 m/s.****Solution:**

Momentum = mass x velocity = 600 x 30 kg m/s = 18000 kg m/s

**5 ] A force of 20 N acts on a rocket for 250 seconds, causing the rocket’s velocity to increasea) Calculate the impulse of the forceb) By how much does the rocket’s momentum increase?**

**Solution:**

a) The impulse of the force = force x time = 20 x 250 Ns = 5000 N s.

b) We know, the

**impulse of the force = change in momentum,**

As here, the rocket’s velocity increases, therefore the rocket’s momentum increases.

And, the Rocket’s momentum increase = impulse of the force applied = 5000 kg m/s.

**6**] **A 10 kg body is moving with a constant acceleration of 4 m/s^2. If the initial velocity of the body is 2 m/s, what is the change in momentum in 5 s?**

Mass of the body (m)= 10kg

Acceleration of the body(a)= 4m/s^2

Initial velocity of the body (u)=2m/s

Change in momentum after time t=5s

(∆p)=?

**Solution**:

*Method 1*

Final velocity: v = u + at

v = 2 + 4 × 5

v = 2 + 20

**v = 22m/s**

**Change in momentum** = ∆p= m × v — m × u

∆p = 10 × 22 — 10 × 2

∆p = 220 — 20

∆p = 200 kg.m/s

**Ans) The change in momentum of a body is 200kg.m/s**

*Method 2*

F = m×a

F = 10 × 4

F = 40N

Using the formula: **F = ∆p/t**

∆p = F × t

∆p = 40N × 5s

∆p = 200Ns = 200 kgm/s^2 × s = 200 kg.m/s

Ans) The change in momentum of a body is 200 kg.m/s

**Related Study: **

*Impulse*

*Impulse momentum Theorem*