Calculation of momentum of a body after 1.5 seconds when a force of 20 Newton is applied on it initially at rest

Formula:

Momentum (p) = Force (F) x Time (t)

Given:

Force (F) = 20 N

Time (t) = 1.5 s

Initial velocity (u) = 0 m/s (as the body is initially at rest)

Final velocity (v) = ?

Mass of the body (m) = ? (not given in the question)

Solution:

As the mass of the body is not given in the question, we cannot directly calculate the momentum using the formula. However, we can use the formula for acceleration to find the final velocity and then use the momentum formula.

Formula:

Final velocity (v) = Initial velocity (u) + (Acceleration (a) x Time (t))

Calculation of acceleration:

Formula:

Force (F) = Mass (m) x Acceleration (a)

Rearranging the formula:

Acceleration (a) = Force (F) / Mass (m)

Substituting the given values,

Acceleration (a) = 20 N / m

We cannot solve for acceleration as the mass (m) is not given.

However, we know that the body is initially at rest, so the initial velocity (u) is 0 m/s.

Formula:

Final velocity (v) = Initial velocity (u) + (Acceleration (a) x Time (t))

Substituting the values,

Final velocity (v) = 0 m/s + (20 N / m) x 1.5 s

Final velocity (v) = 30 m/s / m

We still cannot solve for the momentum as the mass is not given.

However, we can rearrange the formula for acceleration to solve for mass.

Formula:

Acceleration (a) = Force (F) / Mass (m)

Rearranging the formula,

Mass (m) = Force (F) / Acceleration (a)

Substituting the values,

Mass (m) = 20 N / (30 m/s / m)

Mass (m) = 0.67 kg

Now we can calculate the momentum using the formula,

Formula:

Momentum (p) = Force (F) x Time (t)

Substituting the values,

Momentum (p) = 20 N x 1.5 s

Momentum (p) = 30 Ns

Therefore, the momentum of the body after 1.5 seconds is 30 Ns.

F=20N
u=0
P=mv--eq1
F=ma
F=m(v-u)/t
m=Ft/v
substitute in eq 1
P=Ft/v×v
so,
P=Ft
P=20×1.5=3N