A car accelerates uniformly from `18kmh^(-1) " to " 72 kmh^(-1)` in 10s. Calculate the acceleration of the car.

Options

A. `1.5 ms^(2)`
B. `15 ms^(-2)`
C. `15 ms^(-1)`
D. `1.5 ms^(-2)`

Answer

To solve the problem of calculating the acceleration of a car that accelerates uniformly from 18 km/h to 72 km/h in 10 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the speeds from km/h to m/s**:
- To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{1}{3.6} \text{ m/s} \]
- For the initial speed (u):
\[ u = 18 \text{ km/h} = 18 \times \frac{1}{3.6} \text{ m/s} = 5 \text{ m/s} \]
- For the final speed (v):
\[ v = 72 \text{ km/h} = 72 \times \frac{1}{3.6} \text{ m/s} = 20 \text{ m/s} \]

2. **Use the formula for acceleration**:
- The formula for acceleration (a) is given by:
\[ a = \frac{v - u}{t} \]
- Where:
- \( v \) is the final velocity (20 m/s)
- \( u \) is the initial velocity (5 m/s)
- \( t \) is the time taken (10 s)

3. **Substitute the values into the formula**:
- Now we can substitute the values into the acceleration formula:
\[ a = \frac{20 \text{ m/s} - 5 \text{ m/s}}{10 \text{ s}} = \frac{15 \text{ m/s}}{10 \text{ s}} = 1.5 \text{ m/s}^2 \]

4. **Conclusion**:
- The acceleration of the car is \( 1.5 \text{ m/s}^2 \).

### Final Answer:
The acceleration of the car is \( 1.5 \text{ m/s}^2 \).

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