An object of mass 10kg moves at a constant speed of 10 `ms^(-1)`. A constant force, that acts for 4 sec on the object, gives it a speed of `2ms^(-1)` in opposite direction. The force acting on the object is `:`

Options

A. `-3N`
B. `-30N`
C. 3N
D. 30N

Answer

To solve the problem, we need to find the force acting on the object given its mass, initial speed, final speed, and the time duration for which the force acts.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the object, \( m = 10 \, \text{kg} \)
- Initial speed, \( u = 10 \, \text{m/s} \) (in the positive direction)
- Final speed, \( v = -2 \, \text{m/s} \) (in the opposite direction, hence negative)
- Time duration, \( t = 4 \, \text{s} \)

2. **Calculate the Change in Momentum:**
The change in momentum (\( \Delta p \)) can be calculated using the formula:
\[ \Delta p = m(v - u) \]
Substituting the values:
\[ \Delta p = 10 \, \text{kg} \times (-2 \, \text{m/s} - 10 \, \text{m/s}) = 10 \, \text{kg} \times (-12 \, \text{m/s}) = -120 \, \text{kg m/s} \]

3. **Calculate the Force:**
The force (\( F \)) can be calculated using the formula:
\[ F = \frac{\Delta p}{t} \]
Substituting the values:
\[ F = \frac{-120 \, \text{kg m/s}}{4 \, \text{s}} = -30 \, \text{N} \]

4. **Interpret the Result:**
The negative sign indicates that the force is acting in the opposite direction of the initial motion of the object.

### Final Answer:
The force acting on the object is \( -30 \, \text{N} \) (30 N in the opposite direction).

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