A car of mass one metric ton accelerates from rest at the rate of `2m//s^2` from t=0 sec to t=10sec. There after it travels with a uniform velocity. The measure of net retarding force acting on the car after 10 sec is

Options

A. 4000N
B. 2000N
C. 0N
D. `-2000N`

Answer

To solve the problem step by step, we will analyze the motion of the car and apply Newton's laws of motion to find the net retarding force acting on the car after 10 seconds.

### Step 1: Understand the motion of the car
The car starts from rest and accelerates at a rate of \(2 \, \text{m/s}^2\) for the first 10 seconds. After this period, it travels with a uniform velocity.

### Step 2: Calculate the final velocity after 10 seconds
Using the formula for final velocity when starting from rest:
\[ v = u + at \]
where:
- \(u = 0 \, \text{m/s}\) (initial velocity, since the car starts from rest),
- \(a = 2 \, \text{m/s}^2\) (acceleration),
- \(t = 10 \, \text{s}\) (time).

Substituting the values:
\[ v = 0 + (2 \, \text{m/s}^2)(10 \, \text{s}) = 20 \, \text{m/s} \]
So, the final velocity of the car after 10 seconds is \(20 \, \text{m/s}\).

### Step 3: Determine the state of motion after 10 seconds
After 10 seconds, the car travels with a uniform velocity of \(20 \, \text{m/s}\). This means that the velocity does not change, and therefore, the acceleration is \(0 \, \text{m/s}^2\).

### Step 4: Apply Newton's second law to find the net force
According to Newton's second law:
\[ F = ma \]
where:
- \(F\) is the net force,
- \(m\) is the mass of the car,
- \(a\) is the acceleration.

The mass of the car is given as \(1 \, \text{metric ton} = 1000 \, \text{kg}\). Since the car is moving with uniform velocity after 10 seconds, the acceleration \(a = 0 \, \text{m/s}^2\).

Substituting the values into the equation:
\[ F = 1000 \, \text{kg} \times 0 \, \text{m/s}^2 = 0 \, \text{N} \]

### Conclusion
The measure of the net retarding force acting on the car after 10 seconds is \(0 \, \text{N}\).

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