A car increases its speed from ` 20 km//h` to `50 km//h` in `10` seconds. What is its acceleration?

Options

A. 0.5 units
B. 0.83 units
C. 0.91 units
D. None of these

Explanation

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

### Step 1: Identify the initial and final speeds
- The initial speed (u) of the car is 20 km/h.
- The final speed (v) of the car is 50 km/h.

### Step 2: Convert speeds from km/h to m/s
To convert km/h to m/s, we can use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

- **Convert initial speed (u)**:
\[ u = 20 \text{ km/h} \times \frac{5}{18} = \frac{100}{18} \text{ m/s} = \frac{50}{9} \text{ m/s} \]

- **Convert final speed (v)**:
\[ v = 50 \text{ km/h} \times \frac{5}{18} = \frac{250}{18} \text{ m/s} = \frac{125}{9} \text{ m/s} \]

### Step 3: Use the formula for acceleration
Acceleration (a) is defined as the change in velocity over time. The formula is:
\[ a = \frac{v - u}{t} \]
where:
- \( v \) = final velocity = \( \frac{125}{9} \) m/s
- \( u \) = initial velocity = \( \frac{50}{9} \) m/s
- \( t \) = time taken = 10 seconds

### Step 4: Substitute the values into the formula
\[ a = \frac{\frac{125}{9} - \frac{50}{9}}{10} \]

### Step 5: Simplify the equation
- Calculate the change in velocity:
\[ v - u = \frac{125}{9} - \frac{50}{9} = \frac{125 - 50}{9} = \frac{75}{9} \text{ m/s} \]

- Now substitute back into the acceleration formula:
\[ a = \frac{\frac{75}{9}}{10} = \frac{75}{90} = \frac{5}{6} \text{ m/s}^2 \approx 0.83 \text{ m/s}^2 \]

### Final Answer
The acceleration of the car is approximately \( 0.83 \text{ m/s}^2 \).

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