A car accelerates by `50 m//s^(2). It would, attain a speed of 100 km per hour from rest in

Options

A. 0.28 s
B. 0.56 s
C. 1.12 s
D. 2.00 s

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Identify the given values
- Acceleration (a) = 50 m/s²
- Initial velocity (u) = 0 m/s (since the car starts from rest)
- Final velocity (v) = 100 km/h

### Step 2: Convert the final velocity from km/h to m/s
To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ v = 100 \text{ km/h} \times \frac{5}{18} = \frac{500}{18} \text{ m/s} \approx 27.78 \text{ m/s} \]

### Step 3: Use the first equation of motion
The first equation of motion relates the final velocity, initial velocity, acceleration, and time:
\[ v = u + at \]
Substituting the known values:
\[ 27.78 = 0 + 50t \]

### Step 4: Solve for time (t)
Rearranging the equation to solve for time (t):
\[ t = \frac{v - u}{a} = \frac{27.78 - 0}{50} = \frac{27.78}{50} \]
Calculating this gives:
\[ t \approx 0.5556 \text{ seconds} \]
Rounding this to two decimal places:
\[ t \approx 0.56 \text{ seconds} \]

### Final Answer
The time taken for the car to attain a speed of 100 km/h from rest is approximately **0.56 seconds**.

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