A car travelling with a velocity of 80 km/h slowed down to 44 km/h in 15 s. The retardation is

Options

A. `0.67 ms^(-2)`
B. `1 ms^(-2)`
C. `1.25 ms^(-2)`
D. `1.5 ms^(-2)`

Explanation

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

### Step 1: Identify the given values
- Initial velocity (u) = 80 km/h
- Final velocity (v) = 44 km/h
- Time taken (t) = 15 s

### Step 2: Convert velocities from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).

- Initial velocity in m/s:
\[ u = 80 \, \text{km/h} \times \frac{5}{18} = \frac{400}{18} \approx 22.22 \, \text{m/s} \]

- Final velocity in m/s:
\[ v = 44 \, \text{km/h} \times \frac{5}{18} = \frac{220}{18} \approx 12.22 \, \text{m/s} \]

### Step 3: Calculate the change in velocity
The change in velocity (Δv) is given by:
\[ \Delta v = v - u \]
Substituting the values:
\[ \Delta v = 12.22 \, \text{m/s} - 22.22 \, \text{m/s} = -10 \, \text{m/s} \]

### Step 4: Calculate the acceleration (or retardation)
Acceleration (a) is calculated using the formula:
\[ a = \frac{\Delta v}{t} \]
Substituting the values:
\[ a = \frac{-10 \, \text{m/s}}{15 \, \text{s}} = -0.67 \, \text{m/s}^2 \]

### Step 5: Interpret the result
The negative sign indicates that this is a retardation (deceleration). Therefore, the retardation of the car is:
\[ \text{Retardation} = 0.67 \, \text{m/s}^2 \]

### Final Answer
The retardation of the car is \( 0.67 \, \text{m/s}^2 \).

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