A particle had a speed of 18 m/s at a certain time, and 2.5 s later its speed was 30 m/s in the opposite direction. The average acceleration of the particle in the duration is :

Options

A. ` 19.2 m//s^(2) ` in the direction of initial velocity
B. ` 19.2 m//s^(2) ` in the direction opposite to the initial velocity
C. ` 4.8 m//s^(2) ` in the direction of initial velocity
D. ` 4.8 m//s^(2) ` in the direction opposite to the initial velocity

Explanation

To find the average acceleration of the particle, we can follow these steps:

### Step 1: Identify the initial and final velocities
- The initial velocity \( V_i \) is given as 18 m/s (in a certain direction).
- The final velocity \( V_f \) is given as 30 m/s in the opposite direction. Since it is in the opposite direction, we will consider it as negative: \( V_f = -30 \) m/s.

### Step 2: Calculate the change in velocity
- The change in velocity \( \Delta V \) can be calculated using the formula:
\[ \Delta V = V_f - V_i \]
- Substituting the values:
\[ \Delta V = -30 \, \text{m/s} - 18 \, \text{m/s} = -48 \, \text{m/s} \]

### Step 3: Determine the time interval
- The time interval \( t \) is given as 2.5 seconds.

### Step 4: Calculate the average acceleration
- The average acceleration \( a_{avg} \) can be calculated using the formula:
\[ a_{avg} = \frac{\Delta V}{t} \]
- Substituting the values:
\[ a_{avg} = \frac{-48 \, \text{m/s}}{2.5 \, \text{s}} = -19.2 \, \text{m/s}^2 \]

### Step 5: Interpret the result
- The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.

### Final Answer
- The average acceleration of the particle is \( -19.2 \, \text{m/s}^2 \).

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