A6-n force pushes to the right on a 3-kg object for 8 seconds.
a) calculate the impulse.
b) how much momentum did the object gain?

a) The impulse is 48 Ns

b) The momentum the object gained is 48 kgms⁻¹

From the question,

We are to calculate the impulse

Impulse can calculated by using the formula,

I = Ft

Where

I is the impulse

F is the force

and t is the time

From the given information,

F = 6 N

t = 8 secs

Therefore,

I = 6 × 8

I = 48 Ns

The impulse is 48 Ns

b) To determine how much momentum the object gained.

Momentum is given as by the product of mass and change in velocity.

That is,

Momentum = m(v -u)

Where

m is the mass

v is the final velocity

and u is the initial velocity

From Sir Isaac Newton's second law of motion equation, we have that

F = ma

Where F is the force

m is the mass

and a is the acceleration

But, acceleration, a, is given by

Therefore, the equation becomes

This can be written as

Since, I = Ft

Then,

This means

Impulse = Momentum

Thus,

The momentum the object gained is 48 kgms⁻¹

Learn more on calculating impulse here: link

Impulse = 48 kg m/s

Gain in momentum = 48 kg m/s

Explanation:

Force (F) = 6N

Time (t) = 8

Mass (m) = 3 kg

Final velocity (v) = ?

Initial velocity (u) = 0 m/s

First, find acceleration

F = m * a

a = F / m

a = 6 / 3

a = 2 m/s^2

Now, find final velocity

v = u + a * t

v = 0 + 2 * 8

v = 16 m/s

Now, find impulse

Impulse = change in momentum

Impulse = final momentum - initial momentum

Impulse = m * v - m * u

Impulse = m ( v - u )

Impulse = 3 ( 16 - 0 )

Impulse = 48 kg m/s

Here, gain in momentum is same as impulse.

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