A car accelerates uniformly from 18 `kmh^(- 1) to 72 (kmh^- 1) `in 5 s. The acceleration of the car is:

Options

A. 3 `ms^ 2`
B. `10.8 ms^(-2)`
C. `10.8 ms ^2`
D. `3 ms ^(-2)`

Answer

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

### Step 1: Convert the initial and final velocities from km/h to m/s
- Given:
- Initial velocity \( V_i = 18 \, \text{km/h} \)
- Final velocity \( V_f = 72 \, \text{km/h} \)

- Conversion factor:
\[ 1 \, \text{km/h} = \frac{10}{36} \, \text{m/s} \]

- Convert \( V_i \):
\[ V_i = 18 \times \frac{10}{36} = 5 \, \text{m/s} \]

- Convert \( V_f \):
\[ V_f = 72 \times \frac{10}{36} = 20 \, \text{m/s} \]

### Step 2: Use the formula for acceleration
- The formula relating initial velocity, final velocity, acceleration, and time is:
\[ V_f = V_i + a \cdot t \]
where:
- \( a \) is the acceleration
- \( t \) is the time (given as 5 seconds)

### Step 3: Rearrange the formula to solve for acceleration
- Rearranging gives:
\[ a = \frac{V_f - V_i}{t} \]

### Step 4: Substitute the values into the formula
- Substitute \( V_f = 20 \, \text{m/s} \), \( V_i = 5 \, \text{m/s} \), and \( t = 5 \, \text{s} \):
\[ a = \frac{20 - 5}{5} = \frac{15}{5} = 3 \, \text{m/s}^2 \]

### Step 5: Conclusion
- The acceleration of the car is:
\[ a = 3 \, \text{m/s}^2 \]