An object is moving velocity `10 ms^(-1)` . A constant force acts for 4 s object and given it a speed of `2 ms^(-1)` in opposite direction. The acceleration produced is

Options

A. `3 ms^(-2)`
B. `-3 ms^(-2)`
C. `6 ms^(-2)`
D. `-6ms^(-2)`

Explanation

To find the acceleration produced when a constant force acts on an object, we can use the equation of motion:

\[ v = u + at \]

Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step-by-Step Solution:

1. **Identify the Initial and Final Velocities:**
- The initial velocity \( u = 10 \, \text{m/s} \) (in the positive direction).
- The final velocity \( v = -2 \, \text{m/s} \) (in the opposite direction, hence negative).

2. **Identify the Time Duration:**
- The time \( t = 4 \, \text{s} \).

3. **Substitute the Values into the Equation:**
- We can rearrange the equation \( v = u + at \) to solve for acceleration \( a \):
\[ a = \frac{v - u}{t} \]

4. **Plug in the Values:**
- Substitute \( v = -2 \, \text{m/s} \), \( u = 10 \, \text{m/s} \), and \( t = 4 \, \text{s} \):
\[ a = \frac{-2 - 10}{4} \]

5. **Calculate the Acceleration:**
- Simplifying the equation:
\[ a = \frac{-12}{4} = -3 \, \text{m/s}^2 \]

### Final Answer:
The acceleration produced is \( -3 \, \text{m/s}^2 \).

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