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Question: A force acts on a body of mass \(3\,kg\) such that its velocity changes from \(4\,m/s\) to \(10\,m/s...

A force acts on a body of mass 3 kg3\,kg such that its velocity changes from 4 m/s4\,m/s to 10 m/s10\,m/s. What is the change in momentum of the body?
A. 42 kg m/s42\,kg\,m/s
B. 2 kg m/s2\,kg\,m/s
C. 18 kg m/s18\,kg\,m/s
D. 14 kg m/s14\,kg\,m/s

Explanation

Solution

Hint- We know that the momentum can be calculated as a product of mass and velocity. First calculate the initial momentum and then calculate the final momentum. The difference between the final momentum and initial momentum will give us the change in momentum.

Complete step by step answer:
It is given that a force acts on a body which results in a change in velocity.
The mass of the body is given as
m=3 kgm = 3\,kg
The initial velocity of the body is
vi=4 m/s{v_i} = 4\,m/s
After the application of force, the velocity changes. The final value of velocity is given as
vf=10 m/s{v_f} = 10\,m/s
We are asked to calculate the change in momentum of the body due to the applied force.
We know that momentum is the product of mass and velocity of the body.
In equation form we can write momentum as
P=mvP = mv
Where, m is the mass, v is the velocity.
Let us calculate the initial momentum of the body.
Let it be denoted as Pi{P_i} .
Thus,
Pi=mvi{P_i} = m{v_i}
On substituting the values, we get the initial momentum as
Pi=3×4=12 kg m/s{P_i} = 3 \times 4 = 12\,kg\,m/s
Now let us calculate the final momentum, Pf{P_f} .
Pf=mvf{P_f} = m{v_f}
on substituting the values, we get the final momentum as
Pf=3×10=30 kg m/s{P_f} = 3 \times 10 = 30\,kg\,m/s
We want to find the value of change in momentum.
This can be found by subtracting the initial momentum from the final momentum.
That is,
ΔP=Pf−Pi\Delta P = {P_f} - {P_i}
On substituting the values, we get
ΔP=30−12\Delta P = 30 - 12
⇒ΔP=18 kg m/s\Rightarrow \Delta P = 18\,kg\,m/s
This is the total change in momentum due to the applied force.

So, the correct answer is option C.

Note: The value that we calculated is also the value of impulse. An impulse is the product of force and the time of application of force. From Newton's second law we know force is the rate of change of momentum.
F=ΔPΔtF = \dfrac{{\Delta P}}{{\Delta t}}
⇒ΔP=FΔt\Rightarrow \Delta P = F\Delta t
The right-hand side is the same as the impulse. Thus, impulse and change in momentum are equivalent.