A car having a mass of 1000 kg is moving at a speed of `30 "metres"//"sec"`. Brakes are applied to bring the car to rest. If the frictional force between the tyres and the road surface is 5000 newtons, the car will come to rest in

Explanation

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

### Step 1: Identify the given data
- Mass of the car (m) = 1000 kg
- Initial speed of the car (u) = 30 m/s
- Frictional force (F_friction) = 5000 N

### Step 2: Calculate the acceleration
Using Newton's second law of motion, we know that:
\[ F = m \cdot a \]
Where:
- F is the net force acting on the car (which is the frictional force in this case),
- m is the mass of the car,
- a is the acceleration.

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{5000 \, \text{N}}{1000 \, \text{kg}} = 5 \, \text{m/s}^2 \]

Since the car is coming to rest, this acceleration will be negative (deceleration):
\[ a = -5 \, \text{m/s}^2 \]

### Step 3: Use the equations of motion to find the time
We will use the first equation of motion:
\[ v = u + at \]
Where:
- v is the final velocity (0 m/s, since the car comes to rest),
- u is the initial velocity (30 m/s),
- a is the acceleration (-5 m/s²),
- t is the time taken to come to rest.

Substituting the known values into the equation:
\[ 0 = 30 + (-5)t \]

### Step 4: Solve for time (t)
Rearranging the equation:
\[ -5t = -30 \]
\[ t = \frac{-30}{-5} \]
\[ t = 6 \, \text{seconds} \]

### Final Answer
The car will come to rest in **6 seconds**.

---