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 find the force acting on the object, we can use Newton's second law of motion and the concept of impulse. Here's a step-by-step solution:

### Step 1: Identify the initial and final velocities
- The initial velocity (u) of the object is 10 m/s (in one direction).
- The final velocity (v) of the object is -2 m/s (in the opposite direction).

### Step 2: Calculate the change in velocity
The change in velocity (Δv) can be calculated as:
\[ \Delta v = v - u = -2 \, \text{m/s} - 10 \, \text{m/s} = -12 \, \text{m/s} \]

### Step 3: Calculate the acceleration
Using the formula for acceleration (a), we can relate it to the change in velocity over time (t):
\[ a = \frac{\Delta v}{t} \]
Given that the time (t) is 4 seconds:
\[ a = \frac{-12 \, \text{m/s}}{4 \, \text{s}} = -3 \, \text{m/s}^2 \]

### Step 4: Use Newton's second law to find the force
According to Newton's second law:
\[ F = m \cdot a \]
Where:
- \( m = 10 \, \text{kg} \) (mass of the object)
- \( a = -3 \, \text{m/s}^2 \) (acceleration)

Substituting the values:
\[ F = 10 \, \text{kg} \cdot (-3 \, \text{m/s}^2) = -30 \, \text{N} \]

### Step 5: Interpret the result
The negative sign indicates that the force is acting in the opposite direction to the initial motion of the object.

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

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