A car increases its speed form 20km/h to 50km/h in 10 seconds. Its acceleration is

Options

A. `30ms^(-2)`
B. `3ms^(-2)`
C. `18ms^(-2)`
D. none of these

Answer

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

### Step 1: Identify the initial and final velocities
- The initial velocity \( u \) is given as 20 km/h.
- The final velocity \( v \) is given as 50 km/h.

### Step 2: Convert the velocities from km/h to m/s
- To convert km/h to m/s, we use the conversion factor \( \frac{1000 \text{ m}}{3600 \text{ s}} \) or equivalently \( \frac{5}{18} \).
- For the initial velocity:
\[ u = 20 \text{ km/h} \times \frac{5}{18} = \frac{100}{18} \text{ m/s} \]
- For the final velocity:
\[ v = 50 \text{ km/h} \times \frac{5}{18} = \frac{250}{18} \text{ m/s} \]

### Step 3: Use the formula for acceleration
- The formula for acceleration \( a \) is given by:
\[ a = \frac{v - u}{t} \]
where \( t \) is the time taken for the change in velocity.

### Step 4: Substitute the values into the formula
- The time \( t \) is given as 10 seconds.
- Now substituting the values:
\[ a = \frac{\frac{250}{18} - \frac{100}{18}}{10} \]
\[ a = \frac{\frac{150}{18}}{10} \]
\[ a = \frac{150}{18 \times 10} = \frac{150}{180} = \frac{5}{6} \text{ m/s}^2 \]

### Step 5: Conclusion
- The acceleration of the car is \( \frac{5}{6} \text{ m/s}^2 \).