A car is moving with a velocity of 10 m/s. Suddenly driver sees a child at a distance of 30 m and he applies the brakes, it produced a uniform retardation in car and car stops in 5 second. Find (mass of car=1000 kg)
the stopping distance of car
will the car hit the child
the retardation in car
resistive force on car

Answer

To solve the problem step by step, we will break it down into parts as per the questions asked.

### Given Data:
- Initial velocity of the car, \( u = 10 \, \text{m/s} \)
- Final velocity of the car, \( v = 0 \, \text{m/s} \) (since the car stops)
- Time taken to stop, \( t = 5 \, \text{s} \)
- Distance to the child, \( d = 30 \, \text{m} \)
- Mass of the car, \( m = 1000 \, \text{kg} \)

### Step 1: Calculate the Retardation
Using the equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 0 = 10 + a \cdot 5 \]
Rearranging gives:
\[ a \cdot 5 = -10 \implies a = -\frac{10}{5} = -2 \, \text{m/s}^2 \]
Thus, the retardation \( a = 2 \, \text{m/s}^2 \).

### Step 2: Calculate the Stopping Distance
Using the equation:
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ 0 = (10)^2 + 2(-2)s \]
This simplifies to:
\[ 0 = 100 - 4s \implies 4s = 100 \implies s = \frac{100}{4} = 25 \, \text{m} \]
Thus, the stopping distance of the car is \( 25 \, \text{m} \).

### Step 3: Determine if the Car Hits the Child
The distance to the child is \( 30 \, \text{m} \) and the stopping distance of the car is \( 25 \, \text{m} \). Since \( 25 \, \text{m} < 30 \, \text{m} \), the car will stop before hitting the child.

### Step 4: Calculate the Resistive Force on the Car
The resistive force \( F_R \) can be calculated using Newton's second law:
\[ F = ma \]
Substituting the known values:
\[ F_R = 1000 \times (-2) = -2000 \, \text{N} \]
Thus, the resistive force on the car is \( 2000 \, \text{N} \) (acting in the opposite direction of motion).

### Summary of Results:
1. **Stopping Distance of Car**: \( 25 \, \text{m} \)
2. **Will the Car Hit the Child?**: No
3. **Retardation in Car**: \( 2 \, \text{m/s}^2 \)
4. **Resistive Force on Car**: \( 2000 \, \text{N} \)