A man moves on his motorbike with `54 km//h` and then takes a U-turn and continues to move with same velocity The time of U-turn is `10 s`. Find the magnitude of average acceleration during U-turn.

Options

A. 0
B. `3 ms^-2`
C. `1.5 sqrt(2) ms^-2`
D. none of these

Explanation

To find the magnitude of the average acceleration during the U-turn, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The initial speed of the motorbike is given as \(54 \text{ km/h}\). We need to convert this speed into meters per second (m/s) using the conversion factor \(1 \text{ km/h} = \frac{5}{18} \text{ m/s}\).

\[ \text{Speed in m/s} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 2: Determine the initial and final velocities
- The initial velocity \(V_1\) when the man is moving straight is \(15 \text{ m/s}\) in the negative direction (let's assume this is along the negative x-axis, so \(V_1 = -15 \text{ m/s}\)).
- After the U-turn, the final velocity \(V_2\) is \(15 \text{ m/s}\) in the positive direction (along the positive x-axis, so \(V_2 = 15 \text{ m/s}\)).

### Step 3: Calculate the change in velocity
The change in velocity \(\Delta V\) can be calculated as follows:

\[ \Delta V = V_2 - V_1 = 15 - (-15) = 15 + 15 = 30 \text{ m/s} \]

### Step 4: Calculate the average acceleration
The average acceleration \(a\) is given by the formula:

\[ a = \frac{\Delta V}{\Delta t} \]

where \(\Delta t\) is the time taken for the U-turn, which is \(10 \text{ seconds}\).

Substituting the values we have:

\[ a = \frac{30 \text{ m/s}}{10 \text{ s}} = 3 \text{ m/s}^2 \]

### Step 5: Find the magnitude of the average acceleration
The magnitude of the average acceleration is simply the absolute value of the calculated acceleration, which is:

\[ |a| = 3 \text{ m/s}^2 \]

### Final Answer
The magnitude of the average acceleration during the U-turn is \(3 \text{ m/s}^2\).

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