A car accelerates uniformly from rest to a speed of `10 m//s` in a time of 5 s .The number of revolutions made by one of its wheels during this motion if the radius of the wheel is `1//pi` m .

Options

A. 50
B. 25
C. 12.5
D. 6.25

Explanation

To solve the problem step by step, we will follow the physics concepts of uniform acceleration and circular motion.

### Step 1: Determine the acceleration of the car.
The car accelerates uniformly from rest (initial velocity \( u = 0 \)) to a final speed \( v = 10 \, \text{m/s} \) in a time \( t = 5 \, \text{s} \).

Using the formula for acceleration:
\[ v = u + at \]
Substituting the known values:
\[ 10 = 0 + a \cdot 5 \]
Solving for \( a \):
\[ a = \frac{10}{5} = 2 \, \text{m/s}^2 \]

### Step 2: Calculate the distance covered by the car.
Using the formula for distance under uniform acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = 0 \cdot 5 + \frac{1}{2} \cdot 2 \cdot (5^2) \]
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 25 \]
\[ s = 25 \, \text{m} \]

### Step 3: Calculate the circumference of the wheel.
The radius of the wheel is given as \( r = \frac{1}{\pi} \, \text{m} \). The circumference \( C \) of the wheel can be calculated using the formula:
\[ C = 2 \pi r \]
Substituting the radius:
\[ C = 2 \pi \left(\frac{1}{\pi}\right) \]
\[ C = 2 \, \text{m} \]

### Step 4: Calculate the number of revolutions made by the wheel.
To find the number of revolutions \( N \), we divide the total distance covered by the circumference of the wheel:
\[ N = \frac{s}{C} \]
Substituting the values:
\[ N = \frac{25}{2} \]
\[ N = 12.5 \]

### Final Answer:
The number of revolutions made by one of the wheels during this motion is **12.5 revolutions**.

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