A car moving with a speed of 30 `ms^(-1)` takes a U-turn in 6 seconds, without changing its speed. What is the average acceleration during these 6 seconds?

Options

A. `5 ms^(-2)`
B. `10 ms^(-2)`
C. `2.5 ms^(-2)`
D. Zero

Explanation

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

### Step 1: Identify the initial and final velocities
- The car is moving initially at a speed of 30 m/s in one direction.
- After taking a U-turn, the car is still moving at a speed of 30 m/s but in the opposite direction.

### Step 2: Determine the change in velocity
- The initial velocity (u) is +30 m/s (considering the initial direction as positive).
- The final velocity (v) after the U-turn is -30 m/s (since it is now in the opposite direction).
- The change in velocity (Δv) can be calculated as:
\[ \Delta v = v - u = -30 \, \text{m/s} - 30 \, \text{m/s} = -60 \, \text{m/s} \]

### Step 3: Determine the time interval
- The time taken to complete the U-turn is given as 6 seconds.

### Step 4: Calculate the average acceleration
- The formula for average acceleration (a) is given by:
\[ a = \frac{\Delta v}{\Delta t} \]
- Substituting the values we have:
\[ a = \frac{-60 \, \text{m/s}}{6 \, \text{s}} = -10 \, \text{m/s}^2 \]

### Step 5: Interpret the result
- The negative sign indicates that the acceleration is in the opposite direction of the initial motion, which is expected since the car is changing direction.

### Final Answer
The average acceleration of the car during the U-turn is \( -10 \, \text{m/s}^2 \).

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