The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 2 s
(a) What is the momentum before the force acts?
(b) What is the momentum after the force acts ?
(c ) What is the gain in momentum per second ?
(d) what is the value of the force ?

Answer

To solve the problem step by step, we will address each part of the question systematically.

### Given Data:
- Mass of the body (m) = 10 kg
- Initial velocity (u) = 4 m/s
- Final velocity (v) = 8 m/s
- Time (t) = 2 s

### (a) What is the momentum before the force acts?
Momentum (p) is calculated using the formula:
\[ p = m \times v \]
Before the force acts, the velocity is the initial velocity (u).

1. Calculate the momentum before the force acts:
\[ p_{initial} = m \times u = 10 \, \text{kg} \times 4 \, \text{m/s} = 40 \, \text{kg m/s} \]

### (b) What is the momentum after the force acts?
After the force acts, the velocity is the final velocity (v).

2. Calculate the momentum after the force acts:
\[ p_{final} = m \times v = 10 \, \text{kg} \times 8 \, \text{m/s} = 80 \, \text{kg m/s} \]

### (c) What is the gain in momentum per second?
Gain in momentum is the difference between the final momentum and the initial momentum.

3. Calculate the change in momentum:
\[ \Delta p = p_{final} - p_{initial} = 80 \, \text{kg m/s} - 40 \, \text{kg m/s} = 40 \, \text{kg m/s} \]

4. Calculate the gain in momentum per second:
\[ \text{Gain in momentum per second} = \frac{\Delta p}{t} = \frac{40 \, \text{kg m/s}}{2 \, \text{s}} = 20 \, \text{kg m/s}^2 \]

### (d) What is the value of the force?
According to Newton's second law of motion, force (F) can be calculated using the formula:
\[ F = \frac{\Delta p}{t} \]

5. Since we already calculated the gain in momentum per second, we can directly state:
\[ F = 20 \, \text{N} \]

### Summary of Answers:
- (a) Momentum before the force acts: **40 kg m/s**
- (b) Momentum after the force acts: **80 kg m/s**
- (c) Gain in momentum per second: **20 kg m/s²**
- (d) Value of the force: **20 N**

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