A racing car accelerates on a straight road from rest to a speed of 50 mis in 25 s. Assuming uniform acceleration of the car throughout, the distance covered in this time will be

Options

A. 625 m
B. 1250 m
C. 2500 m
D. 50 m

Explanation

To solve the problem of how far a racing car accelerates from rest to a speed of 50 m/s in 25 seconds with uniform acceleration, we can follow these steps:

### Step 1: Identify the known values
- Initial velocity (u) = 0 m/s (since the car starts from rest)
- Final velocity (v) = 50 m/s
- Time (t) = 25 s

### Step 2: Calculate the acceleration (a)
Using the first equation of motion:
\[ v = u + at \]

Substituting the known values:
\[ 50 = 0 + a \cdot 25 \]

Rearranging to find acceleration (a):
\[ a = \frac{50}{25} = 2 \, \text{m/s}^2 \]

### Step 3: Calculate the distance covered (s)
Using the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]

Since the initial velocity (u) is 0:
\[ s = 0 \cdot t + \frac{1}{2} a t^2 \]
\[ s = \frac{1}{2} \cdot 2 \cdot (25)^2 \]

Calculating the distance:
\[ s = 1 \cdot 625 = 625 \, \text{m} \]

### Final Answer
The distance covered by the racing car in 25 seconds is **625 meters**.

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