### Momentum:

Momentum of a body is the product of the mass of a body and its linear velocity. The symbol that is used to represent momentum is **p**.

Momentum, p = mass (m) x velocity (v)

p = kg x ms^{-1}.

Its unit is kgms^{-1}. It is a vector quantity.

The momentum of a body depends on the mass and the velocity with which the body is moving. Its direction is the same as the direction of the object’s velocity.

A bus can have a large momentum even if it’s moving slowly because of its **large mass**.

A bullet can have a large momentum even though it has a small mass because it’s moving with a **high velocity.**

If an object is at rest it has no momentum no matter how large its mass is.

In this case mass x 0 velocity = 0 Momentum

**Note:** If you want it in terms of Newton it becomes â€˜newton secondâ€™.

Here is why;

Force = mass Ã— acceleration (a)

Unit of acceleration = m/s^{2}

We know that unit of force is Newton (N) and

1 N = \( \frac{kgm}{s^2}\) ….(1)

Momentum (p) = mass (m) Ã— velocity (v)

Taking the SI units

Unit of mass = kg

Unit of velocity = m/s

So

P* *= \( \frac{kgm}{s}\)

Suibstitute in equation (1)

F = N = \( \frac{kgm}{s^2}\\ = \frac{kgm}{s \: \times \: s}\\ = \frac{p}{s}\)

if F = \( \frac{p}{s}\)

Then, Momentum, p = Ns

p = Newton Ã— second

### Example 1:

A car of mass 145 g moves with a velocity of 30m/s. Calculate the momentum of the car.

**Solution:**

**Values given:**

Mass = 145 g = Â \( \frac{145}{1000} \) = 0.145 kg

velocity = 30 m/s

momentum = ?

Momentum, p = m x v

p = 0.145 x 30 = 4.35 Nm

Momentum = 4.35 kgm/s

### Example 2:

Given that the momentum of a train is 354 kgm/s, calculate the mass if its velocity is 17.6 m/s.

**Soultion:**

**Values given:**

Momentum = 354 kgm/s

velocity = 17.6 m/s

mass = ?

Momentum, p = mass x velocity

make mass the subject of the formula

mass = \( \frac{momentum}{velocity} \)

mass = \( \frac{354}{17.6} \)

mass = 20.11kg

### Example 3:

A train of mass 6000kg moves with a velocity V. If the momentum of the train is 1000Nm, calculate the velocity of the train.

**Solution:**

**Values given:**

Momentum = 1000 Nm

velocity = ?

mass = 6000kg

Momentum, p = mass x velocity

make velocity the subject of the formula

velocity = \( \frac{momentum}{mass} \)

Substitute in the values

velocity = \( \frac{1000}{6000} \)

velocity = 0.167 m/s

### Example 4:

A body of mass 20kg moves with a velocity of 10ms^{-1}, calculate its linear momentum

**Solution:**

**Values given:**

mass = 20kg

velocity = 10ms^{-1}

Momentum = mass x velocity

= 20kg x 10ms^{-1}

Momentum = 200kgms^{-1}.

### Impulse:

The impulse of a force is the product of average force and the time during which it acts on the body. A force which acts for a very short time is called impulsive force or simply impulse. Impulse is usually associated with collision and is also called a blow

Impulse = Force x time

I = F x t

Impulse = Newton x seconds

I = Ns

The unit of impulse is Ns. It is a vector quantity.

### Example 5:

A force of 40N acts on a body for 5 seconds. What is the impulse experienced?

**Solution:**

**Values given:**

F = 40N, t = 5 secs.

Impulse = Force x time

Impulse = 40 x 5

Â Impulse = 200Ns.

### Example 6:

If a force of 45 N acts on 10.75 kg mass and the impulse is 44.94Ns, calculate the time for which the force acts on the object.

**Solution:**

**Values given: **

Force = 45N

mass = 10.75kg

Impulse = 44.94Ns

Impulse = Force x time

make time the subject of the formula

time = \( \frac{Impulse}{Force} \)

time = \( \frac{44.94}{45} \)

time = \( \frac{44.94}{45} \)

time = 0.998 = 1s

### Example 7:

The impulse of a force is 458 Ns. If the force acts for 1465 seconds, calculate the magnitude of the force.

**Solution:**

**Values given: **

Force = ?, t = 1465 seconds, Impulse = 458 Ns

Impulse = Force x time

make Force the subject of the formula

Force = \( \frac{Impulse}{time} \)

Force = \( \frac{458}{1465} \)

Force = 0.312N

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