A boy is moving westward with a velocity of `10ms^(-1)`. In 20 seconds , velocity changes to `5 ms^(-1)` southwards . Calculate the average acceleration of the boy in this interval

Answer

To solve the problem of calculating the average acceleration of the boy, we will follow these steps:

### Step 1: Identify Initial and Final Velocities
- The initial velocity (\( \vec{u} \)) is given as \( 10 \, \text{m/s} \) westward. In vector form, this can be represented as:
\[ \vec{u} = -10 \hat{i} \, \text{m/s} \]
(where \( \hat{i} \) represents the east direction, thus west is negative).

- The final velocity (\( \vec{v} \)) is given as \( 5 \, \text{m/s} \) southward. In vector form, this can be represented as:
\[ \vec{v} = -5 \hat{j} \, \text{m/s} \]
(where \( \hat{j} \) represents the north direction, thus south is negative).

### Step 2: Calculate Change in Velocity
- The change in velocity (\( \Delta \vec{v} \)) is calculated as:
\[ \Delta \vec{v} = \vec{v} - \vec{u} \]
Substituting the values:
\[ \Delta \vec{v} = (-5 \hat{j}) - (-10 \hat{i}) = 10 \hat{i} - 5 \hat{j} \]

### Step 3: Determine the Time Interval
- The time interval (\( \Delta t \)) is given as \( 20 \, \text{s} \).

### Step 4: Calculate Average Acceleration
- Average acceleration (\( \vec{a}_{avg} \)) is given by the formula:
\[ \vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t} \]
Substituting the values:
\[ \vec{a}_{avg} = \frac{10 \hat{i} - 5 \hat{j}}{20} \]
Simplifying this:
\[ \vec{a}_{avg} = \frac{10}{20} \hat{i} - \frac{5}{20} \hat{j} = 0.5 \hat{i} - 0.25 \hat{j} \, \text{m/s}^2 \]

### Step 5: Final Result
- Therefore, the average acceleration of the boy is:
\[ \vec{a}_{avg} = 0.5 \hat{i} - 0.25 \hat{j} \, \text{m/s}^2 \]