A car of mass m starts from rest and acquires a velocity along east `upsilon = upsilonhati (upsilon gt 0)` in two seconds Assuming the car moves with unifrom acceleration the force exerted on the car is .

Options

A. `(mv)/(2)` eastward and is exerted by the car engine.
B. `(mv)/(2)` eastward and is due to the friction on the tyres exerted by the road.
C. more than `(mv)/(2)` eastward exerted due to the 2 engine and overcomes the friction of the road.
D. `(mv)/(2)` exerted by the engine.

Explanation

To solve the problem step by step, we will use the equations of motion and Newton's second law of motion.

### Step 1: Identify the given information
- Mass of the car = \( m \)
- Initial velocity (\( u \)) = 0 (since the car starts from rest)
- Final velocity (\( v \)) = \( v \hat{i} \) (the car acquires a velocity in the east direction)
- Time (\( t \)) = 2 seconds

### Step 2: Use the equation of motion
We will use the first equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ v \hat{i} = 0 + a \cdot 2 \]
This simplifies to:
\[ v \hat{i} = 2a \hat{i} \]

### Step 3: Solve for acceleration (\( a \))
From the equation \( v \hat{i} = 2a \hat{i} \), we can isolate \( a \):
\[ a = \frac{v}{2} \hat{i} \]

### Step 4: Use Newton's second law to find the force
According to Newton's second law:
\[ F = ma \]
Substituting the expression for acceleration:
\[ F = m \left(\frac{v}{2} \hat{i}\right) \]
This simplifies to:
\[ F = \frac{mv}{2} \hat{i} \]

### Step 5: Conclusion
The force exerted on the car is:
\[ F = \frac{mv}{2} \hat{i} \]
This indicates that the force acts in the eastward direction.