Question

The velocity of a body of mass 5kg changes from 30 m/s to 40 m/s. Find the corresponding increase in its momentum.
A) 50 kg m/s
B) 75 kg m/s
C) 150 kg m/s
D) 300 kg m/s

Answer 1

Linear momentum of a body is the product of the mass of the body and its velocity. It describes how much mass is present in how much motion.

Formulas used:
The momentum $p$ of a body of mass $m$ and velocity $v$ is given by, $p = mv$

Complete step by step answer:
Step 1: List the data given in the question.
The mass of the body is $m = 5{\text{kg}}$ . The change in velocity is from 30 m/s to 40 m/s.
Let ${v_i}$ be the initial velocity and ${v_f}$ be the final velocity of the body. Then we have, ${v_i} = 30{\text{m/s}}$ and ${v_f} = 40{\text{m/s}}$ .
Step 2: Calculate the initial momentum.
The momentum $p$ of a body of mass $m$ and velocity $v$ is given by, $p = mv$ -------- (1)
Let ${p_i}$ be the initial momentum. Then equation (1) will be ${p_i} = m{v_i}$ .
Substituting the values for $m = 5{\text{kg}}$ and ${v_i} = 30{\text{m/s}}$ in the above equation we get, ${p_i} = 5 \times 30 = 150{\text{ kg m/s}}$ .
Thus the initial momentum is ${p_i} = 150{\text{ kg m/s}}$ .
Step 3: Calculate the final momentum.
The momentum $p$ of a body of mass $m$ and velocity $v$ is given by, $p = mv$ -------- (1)
Let ${p_f}$ be the final momentum. Then equation (1) will be ${p_f} = m{v_f}$ .
Substituting the values for $m = 5{\text{kg}}$ and ${v_f} = 40{\text{m/s}}$ in the above equation we get, ${p_f} = 5 \times 40 = 200{\text{ kg m/s}}$ .
Thus the initial momentum is ${p_f} = 200{\text{ kg m/s}}$ .
Step 4: Find the change in momentum.
We have the initial momentum as ${p_i} = 150{\text{ kg m/s}}$ and the final momentum as ${p_f} = 200{\text{ kg m/s}}$ .
Then the change in momentum will be $\Delta p = {p_f} - {p_i}$ -------- (2).
Substituting the values of initial momentum and final momentum in equation (2) we get, $\Delta p = 200 - 150 = 50{\text{ kg m/s}}$

Therefore, the increase in momentum is 50 kg m/s.

Note:
- The change in momentum is referred to as impulse.
- A change in momentum occurs when a force acts on a body for a given time. If force is in a direction opposite to the body’s velocity, then the body slows down.
- If the force acts in the same direction in which the body moves, then the body will speed up. In our problem, the momentum increases since the velocity of the body increases. This suggests that a force acted for a given time in the direction of the body’s motion.