A car having a mass of 1000 kg is moving at a seed 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 reast in

Options

A. 5s
B. 10s
C. 12s
D. 6s

Explanation

To solve the problem, we will follow these steps:

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

### Step 2: Use Newton's second law to find acceleration
According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Here, we can rearrange this to find acceleration (a):

\[ a = \frac{F}{m} \]

Substituting the values we have:

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

Since this is a frictional force acting to stop the car, the acceleration will be negative:

\[ a = -5 \, \text{m/s}^2 \]

### Step 3: Use the kinematic equation to find the time taken to stop
We will use the kinematic equation:

\[ v = u + at \]

Where:
- \(v\) = final velocity = 0 m/s (the car comes to rest)
- \(u\) = initial velocity = 30 m/s
- \(a\) = acceleration = -5 m/s²
- \(t\) = time taken to stop (what we need to find)

Substituting the known values into the equation:

\[ 0 = 30 + (-5)t \]

Rearranging gives:

\[ 5t = 30 \]

Now, solving for \(t\):

\[ t = \frac{30}{5} = 6 \, \text{seconds} \]

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

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